pacman::p_load(tmap, sf, sp, tidyverse, knitr, spflow, Matrix, performance)Prototyping Modules for Geospatial Analytics Shiny Application
1.0 Overview
In the realm of application development, prototyping serves as a powerful tool that breathes life into abstract concepts and ideas, transforming them into tangible representations. It is akin to a bridge that connects the realm of theoretical design with the practical world of user interaction.
A prototype, particularly for an application, is primarily a tool for validating design. It provides a platform to test and verify whether the visual elements and user experience (UX) of the application resonate with stakeholders and potential users. This process is crucial as it allows for the refinement of the application’s UX before further resources are committed, thereby ensuring efficiency and effectiveness in the development process.
1.1 Prototyping for Shiny Application
In the context of developing a Shiny application with R, prototyping takes on a more specific role. It involves evaluating and determining the necessary R packages that are supported in R CRAN, which forms the backbone of the application. This step ensures that the application is built on a solid and reliable foundation.
Furthermore, prototyping involves preparing and testing specific R codes to ensure they run correctly and return the expected output. This step is akin to a rehearsal before the actual performance, ensuring that the final product runs smoothly and meets the desired objectives.
Another critical aspect of prototyping in Shiny application development is determining the parameters and outputs that will be exposed on the Shiny applications. This process is like setting the stage for user interaction, deciding what the users see and how they interact with the application.
Lastly, prototyping involves selecting the appropriate Shiny UI components for exposing the parameters determined above. This step is where the application starts to take shape, and the user interface begins to reflect the application’s functionality and purpose.
In essence, prototyping is a journey of transformation, from abstract ideas to a functional application, ensuring that the final product not only meets design specifications but also provides an engaging and satisfactory user experience. It is the lighthouse that guides the application development process, ensuring that the final product is not just a mere application, but a solution that meets the needs of its users.
This exercise is designed as a comprehensive walk-through of the prototyping process for a Shiny application. It will guide you through each step, starting from the basics of Shiny, moving on to the ideation of a generic design, followed by the analysis of R-packages and testing of R codes, which all will contribute to the proposed storyboard of our Shiny application.
2.0 Understanding Basics of Shiny
Shiny is an open-source R package that provides a powerful web framework for building interactive web applications using R. The best part? We don’t need to dive into all that web design jargon like HTML, CSS, or JavaScript. We just focus on our R analysis, and Shiny turns it into a web app that others can play around with.
2.1 Basic Building Blocks of Shiny
When we’re working with Shiny, we basically have a folder that contains an R script named app.R. This script is the heart of our Shiny application. It’s made up of two main parts: a user interface ui object and a server function.
One of the cool things about Shiny is that it lets us keep our ui object and server function separate. This means we can clearly split up the code that creates our user interface (that’s the front end, what our users see and interact with) from the code that decides how our application behaves (that’s the back end, the behind-the-scenes stuff). It’s like having a clean, organized workspace, which makes our job a whole lot easier!
2.2 UI
When we’re building a Shiny application, we work with three main components headerPanel, sidebarPanel, and mainPanel. These are the building blocks for our app’s user-interface.
Sidebar Panel (
sidebarPanel): This is a vertical panel on the side of the application. It is displayed with a distinct background color and typically contains input controls.Main Panel (
mainPanel): This is the primary area of the application and it typically contains outputs. The main panel displays the output (like maps, plots, tables, etc.) based on the input given in the sidebar panel.Header Panel (
headerPanel): This is the topmost part of the UI where you can place the title of our application. It is not always necessary but can be used to provide a title or brief description of our application.
Grid Layout System: FluidRow and Column
When we’re designing the layout of our Shiny app, we get to play around with two functions fluidRow() and column(). Rows are created using the fluidRow() function. Within these rows, we can add columns - but a thing to note here is that columns can only be included within a row. We can define columns using the column() function. The width of these columns is based on the Bootstrap 12-wide grid system. This means we can have up to 12 columns in a single row, giving us a lot of flexibility in how we want to arrange things.
By playing around with fluidRow() and column(), we can create a wide variety of layouts. A few examples of different layout grids can be seen below:
Header Panel: Navbar Pages
To create a Shiny application that consists of multiple distinct sub-components (each with their own sidebar, tabsets, or other layout constructs), Shiny provides navbarPage() function to create subsection pages within a single Shiny application. So, no matter how complex our app gets, navbarPage() helps us keep things organized and user-friendly.
Sidebar Panel: User Inputs and Controls
To insert the user input specifications and controls, Shiny provides functions like sliderInput(), selectInput(), textInput(), numericInput(), checkboxInput(), and checkboxGroupInput(), among others. Each of these functions helps us create a different user interface widget for input specifications and controls. Below is a summary of how different functions create user interface widgets for input specifications and controls.
Here are a few functions that are commonly used!
sliderInput(): This function lets us add a slider bar. It’s perfect when we want users to select a value within a range.selectInput(): This function creates a dropdown list. It’s great for when we have a list of options and we want users to select one.textInput(): This function gives us a text box. It’s ideal for when we want users to type in some text.numericInput(): This function creates a numeric input field. It’s useful when we need users to enter a number.checkboxInput(): This function lets us add a checkbox. It’s handy when we want users to make a binary choice.checkboxGroupInput(): This function creates a group of checkboxes. It’s perfect for when we want users to select multiple options from a list.
submitButton() can be used to compile the specified inputs and controls and send to the server to refresh and update the main panel contents.
Main Panel: Outputs
In our Shiny app, we can create placeholders in the main panel for outputs. These are later filled in by the server function, which translates our inputs into outputs. There are three main types of output, which correspond to the three things we usually include in a report: text, tables, and plots. Shiny provides functions like textOutput(), tableOutput(), and plotOutput() to define output elements and renderText(), renderTable() and renderPlot() to render and create output elements on user interface. Using fluidRow() and column(), configurations of the output elements can be customised as well.
Main Panel: Tabsets
Shiny provides tabsetPanel() function that allows us to subdivide the main panel into multiple sections. Each section can then show different outputs. It’s like having different tabs in a browser, each showing a different webpage. This way, we can keep our outputs neat and organized, and our users can easily find what they’re looking for.
2.3 Server
In a Shiny application, the server component is responsible for the server-side logic of our application. The server object can include one or more functions that take the inputs from our ui object and turn them into outputs. A server function usually take in an input and an output parameter. The input parameter allows the server to access the UI inputs, and the output parameter is used to define how to display outputs on the UI. An optional parameter session can also be inputted to define the session-related logic to the application.
So, how do the u and server interact to run the app? Well, imagine it like a two-way street. The ui sends the inputs to the server, and the server sends back the outputs to be displayed on the ui. It’s a continuous loop of interaction that keeps our app running smoothly. A generi diagram of how they interact to run the application has been formulated below:
In actual fact, there are multiple customisation and extensions available in Shiny to improve the look and feel of our application. However, I only covered basic components and certain customisations from my research that I intend to use in my proposed design.
3.0 Analysing R-Packages
There are multiple R-packages available
4.0 Testing Spatial Interaction Modelling
First, import three datasets
flow_data_mergedcontains the origin-destination flow data of public bus trajectories for three months (November, December, and January)od_data_mergedcontains the origin-destination pair of bus stops within Singapore and the associated intra-region, and inter-regional flowhex_grid_pa_szcontains the analytical hexagon division of Singapore for spatial interaction modelling, with geometric data, associated subzone and planning area of each hexagon.
flow_data_merged <- read_rds("~/IS415-GAA/Take-home_Ex/Take-home_Ex03/data/flow_data_merged.rds")
od_data_merged <- read_rds("~/IS415-GAA/Take-home_Ex/Take-home_Ex03/data/od_data.rds")
hex_grid_pa_sz <- read_rds("~/IS415-GAA/Take-home_Ex/Take-home_Ex03/data/hex_grid_pa.rds")4.1 Creating Outflow Map
In this section, we will create outflow map for each hexagon. This map will serve as a visual representation of the total count of outflow movement of people from each hexagon to others.
Our original dataset is quite large, encompassing a vast amount of data. However, for the purpose of prototyping, we will be utilizing only a fragment of this data. This approach allows us to test the functionality of various R packages and assess the types of visualizations and analytical outcomes that can be produced without exhausting computational resources.
For this purpose, I filter the data where DAY_TYPE is “WEEKDAY” and TIME_PER_HOUR is 8, which represents 8 AM in the morning. the resultant data stored as flow_data_weekday_morn. This filtered data, stored as flow_data_weekday_morn, will be used for subsequent map creations.
flow_data_weekday_morn <- flow_data_merged %>% filter(DAY_TYPE == "WEEKDAY", TIME_PER_HOUR %in% c(8))In our dataset, each origin-destination trajectory is represented as individual row. For map creation, we will aggregate the total trips by origin hexagon. This gives us a summary of the total trips that originated from each hexagon - hence providing outflow volume.
outflow_data_weekday_morn <- aggregate(flow_data_weekday_morn$TOTAL_TRIPS, by=list(Category=flow_data_weekday_morn$ORIGIN_hex), FUN=sum)
colnames(outflow_data_weekday_morn) <- c("index", "TOTAL_TRIPS")The newly aggregated dataset that we have is of the data.frame type. While this format is useful for many types of data analysis, it is not directly compatible with mapping functions. Therefore, to facilitate the creation of our outflow maps, we need to join this dataset with the spatial features object hex_grid_pa_sz which is of the sf (simple features) type.
To accomplish this, we will use the left_join() function from the dplyr package in R. The left_join() function merges two datasets together based on a common column. In our case, this common column is the index column. This will result in a new sf object called outflow_data_weekday_morn_hex that contains both the outflow data and the corresponding spatial data for each hexagon.
outflow_data_weekday_morn_hex <- left_join(hex_grid_pa_sz, outflow_data_weekday_morn, by = 'index')It’s crucial to understand that not every hexagon may have an aggregated value, especially considering that we are working with a subset of the original dataset. To address it, any NA values in the TOTAL_TRIPS column of the outflow_data_weekday_morn_hex data frame will be replaced with 0.
outflow_data_weekday_morn_hex$TOTAL_TRIPS <- ifelse(is.na(outflow_data_weekday_morn_hex$TOTAL_TRIPS), 0, outflow_data_weekday_morn_hex$TOTAL_TRIPS)Finally we can prepare the outflow map using the appropriate tmap functions.
tmap_mode("view")
tm_shape(outflow_data_weekday_morn_hex) +
tm_fill(col = "TOTAL_TRIPS",
palette = c("#f2ffff","#f9f777","#f8d673","#f89974","#D66779","#b977cb","#7977f3","#57bfc0"),
style = "fixed",
breaks = c(0,1,100,1000,10000,100000,500000,1000000,5000000),
title = "Outflow Trip Count",
id = "TOTAL_TRIPS") +
tm_borders(col = "grey")
Reflection
Prototyping Thoughts
Notably, style argument is set to “fixed”. This means that the color breaks are manually specified and breaks argument specifies the boundaries (flow volume count) for the color breaks.
I choose to manually specify these color breaks because it helps the users to have a consistent interpretation of the colors across different maps. By using the same color breaks, I ensure that the same range of data values corresponds to the same color on all my maps. This makes it easier for the users to compare maps and understand trends and patterns. For instance, if one color represents a range of 0-10 on one map and 0-20 on another, it would be difficult to make easy and accurate comparisons between the two maps. By using fixed color breaks, I eliminate this issue and make my maps more intuitive and user-friendly.
4.2 Making Inflow Map
Similar to what we did for outflow map, we will follow the same process for inflow map as well. Instead of aggregating the data by original hexagon ORIGIN_hex, we will use DESTIN_hex this time, so that we aggregate the total of inflow movement into each hexagon.
inflow_data_weekday_morn <- aggregate(flow_data_weekday_morn$TOTAL_TRIPS, by=list(Category=flow_data_weekday_morn$DESTIN_hex), FUN=sum)
colnames(inflow_data_weekday_morn) <- c("index", "TOTAL_TRIPS")After aggregation, we implement left_join() with hex_grid_pa_sz and then replace the NULL values with 0.
inflow_data_weekday_morn_hex <- left_join(hex_grid_pa_sz, inflow_data_weekday_morn, by = 'index')
inflow_data_weekday_morn_hex$TOTAL_TRIPS <- ifelse(is.na(inflow_data_weekday_morn_hex$TOTAL_TRIPS), 0, inflow_data_weekday_morn_hex$TOTAL_TRIPS)Finally we can prepare the inflow map using the appropriate tmap functions.
tmap_mode("view")
tm_shape(inflow_data_weekday_morn_hex) +
tm_fill(col = "TOTAL_TRIPS",
palette = c("#f2ffff","#f9f777","#f8d673","#f89974","#D66779","#b977cb","#7977f3","#57bfc0"),
style = "fixed",
breaks = c(0,1,100,1000,10000,100000,500000,1000000,5000000),
title = "Inflow Trip Count",
id = "TOTAL_TRIPS")+
tm_borders(col = "grey")+
tm_layout(legend.title.size = 1,
legend.text.size = 0.6,
frame = TRUE)4.3 Making Distribution Graphs
Another visualisation that can be produced to support the maps created above is a distribution graph. Although the map provides the specifica spatial patterns of the flow volumes, it is not striaghtforward to discent the distribution. In this regards, we will create distribution graphs to supplement the maps.
Reflection
Prototyping Thoughts
When I create distribution graphs to accompany and supplement my maps, I believe it’s of utmost importance to maintain a consistent representation. To achieve this, I’ll create the histograms using the breaks I specified in the maps as bins and use the same color palette. Essentially, I want users to look at the maps and histograms together and receive a consistent message. This way, they can easily interpret the information and understand the patterns I’m trying to highlight.
Here, we will define the breaks, labels and color_map for our distribution graphs. We use the consistent language with the breaks and labels and consistent color palette from the previous overall SIngapore map.
breaks <- c(0,0.9,100,1000,10000,100000,500000,1000000,5000000)
labels <- c("0", "1 to 100", "100 to 1,000", "1,000 to 10,000", "10,000 to 100,000", "100,000 to 500,00", "500,000 to 1,000,000", "1,000,000 to 5,000,000")
colors = c("#f2ffff","#f9f777","#f8d673","#f89974","#D66779","#b977cb","#7977f3","#57bfc0")
color_map = setNames(colors, labels)Outflow Distribution Graph
Using the breaks and labels, we will create a new data column called TRIPS_BIN which categorizes the TOTAL_TRIPS into different bins based on the breaks we defined earlier.
outflow_data_weekday_morn_hex$TRIPS_BIN <- cut(outflow_data_weekday_morn_hex$TOTAL_TRIPS, breaks = breaks, labels=labels, include.lowest = TRUE, right = FALSE)
head(outflow_data_weekday_morn_hex)Simple feature collection with 6 features and 5 fields
Geometry type: POLYGON
Dimension: XY
Bounding box: xmin: 2292.538 ymin: 21664.98 xmax: 3417.538 ymax: 28376.68
Projected CRS: SVY21 / Singapore TM
PLN_AREA_N SUBZONE_N index TOTAL_TRIPS
1 TUAS TUAS VIEW EXTENSION 1 0
2 TUAS TUAS VIEW EXTENSION 2 0
3 TUAS TUAS VIEW EXTENSION 3 0
4 TUAS TUAS VIEW EXTENSION 4 0
5 TUAS TUAS VIEW EXTENSION 5 0
6 TUAS TUAS VIEW EXTENSION 6 0
geometry TRIPS_BIN
1 POLYGON ((2667.538 22314.5,... 0
2 POLYGON ((2667.538 23613.54... 0
3 POLYGON ((2667.538 24912.58... 0
4 POLYGON ((2667.538 26211.61... 0
5 POLYGON ((2667.538 27510.65... 0
6 POLYGON ((3042.538 21664.98... 0Next, we will create distribution graph for outflow map using relevant ggplot2 functions.
ggplot(data = outflow_data_weekday_morn_hex,
aes(y = TRIPS_BIN,fill = TRIPS_BIN)) +
geom_bar(show.legend = FALSE)+
xlab("Count of Analytical Hexagons") +
ylab("Outflow Trip Count") +
scale_fill_manual(values=color_map) +
ggtitle("Distribution of Hexagons Per Each Outflow Trip Count Bin")
Reflection
Prototyping Thoughts
Looking at the graphs above, I noticed that the number of hexagons with zero flow volume significantly outweighs the overall distribution. This makes the differences in other categories appear less significant. To address this, I decided to create a new graph where I exclude the hexagons with zero outflow trips. This will allow me to focus on the hexagons with non-zero outflow trips and gain a better understanding of their distribution.
outflow_data_weekday_morn_nozero <- outflow_data_weekday_morn_hex %>% filter(TOTAL_TRIPS != 0)Next, we will create distribution graph for outflow map using relevant ggplot2 functions.
ggplot(data = outflow_data_weekday_morn_nozero,
aes(y = TRIPS_BIN,fill = TRIPS_BIN)) +
geom_bar(show.legend = FALSE)+
xlab("Count of Analytical Hexagons") +
ylab("Outflow Trip Count") +
scale_fill_manual(values=color_map)+
ggtitle("Distribution of Hexagons Per Each Outflow Trip Count Bin",
subtitle = "(excluding hexagons with zero outflow trip)")
Inflow Distribution Graph
We will repeat the same procedures for inflow distribution graphs as well.
inflow_data_weekday_morn_hex$TRIPS_BIN <- cut(inflow_data_weekday_morn_hex$TOTAL_TRIPS, breaks = breaks, labels=labels, include.lowest = TRUE, right = FALSE)
head(inflow_data_weekday_morn_hex)Simple feature collection with 6 features and 5 fields
Geometry type: POLYGON
Dimension: XY
Bounding box: xmin: 2292.538 ymin: 21664.98 xmax: 3417.538 ymax: 28376.68
Projected CRS: SVY21 / Singapore TM
PLN_AREA_N SUBZONE_N index TOTAL_TRIPS
1 TUAS TUAS VIEW EXTENSION 1 0
2 TUAS TUAS VIEW EXTENSION 2 0
3 TUAS TUAS VIEW EXTENSION 3 0
4 TUAS TUAS VIEW EXTENSION 4 0
5 TUAS TUAS VIEW EXTENSION 5 0
6 TUAS TUAS VIEW EXTENSION 6 0
geometry TRIPS_BIN
1 POLYGON ((2667.538 22314.5,... 0
2 POLYGON ((2667.538 23613.54... 0
3 POLYGON ((2667.538 24912.58... 0
4 POLYGON ((2667.538 26211.61... 0
5 POLYGON ((2667.538 27510.65... 0
6 POLYGON ((3042.538 21664.98... 0ggplot(data = inflow_data_weekday_morn_hex,
aes(y = TRIPS_BIN,fill = TRIPS_BIN)) +
geom_bar(show.legend = FALSE)+
xlab("Count of Analytical Hexagons") +
ylab("Inflow Trip Count") +
scale_fill_manual(values=color_map) +
ggtitle("Distribution of Hexagons Per Each Inflow Trip Count Bin")
inflow_data_weekday_morn_nozero <- inflow_data_weekday_morn_hex %>% filter(TOTAL_TRIPS != 0)ggplot(data = inflow_data_weekday_morn_nozero,
aes(y = TRIPS_BIN,fill = TRIPS_BIN)) +
geom_bar(show.legend = FALSE)+
xlab("Count of Analytical Hexagons") +
ylab("Inflow Trip Count") +
scale_fill_manual(values=color_map)+
ggtitle("Distribution of Hexagons Per Each Inflow Trip Count Bin",
subtitle = "(excluding hexagons with zero inflow trip)")
4.4 Zooming into Planning Areas and Subzones
In this section, we will further zoom our inflow/outflow map into planning areas and subzones.
Reflection
Prototyping Thougths
In the previous section, my focus was on exploring the inflow and outflow maps for the entirety of Singapore Island. However, I realized that this broad perspective might not be intuitive enough to identify patterns at the local subzone levels.
Especially when we’re using analytical hexagons to represent the spatial units, it can pose a real challenge for users to understand the local details. For instance, figuring out which planning area or subzone a hexagon belongs to, or simply pinpointing a planning area or subzone’s location in Singapore, can be quite tricky.
Considering this, I thought of a potential enhancement to the user experience. What if I could allow users to specify the subzone they’re interested in? This way, they could delve into the details of that particular area, examining the inflow and outflow patterns more closely. Not only would this make the data more relevant and personalized for the user, but it could also reveal unique patterns and trends that might be overlooked in a broader analysis.
Before we go about testing, let’s have a quick look at how the structure of our inflow and outflow dataset looks like.
head(inflow_data_weekday_morn_hex)Simple feature collection with 6 features and 5 fields
Geometry type: POLYGON
Dimension: XY
Bounding box: xmin: 2292.538 ymin: 21664.98 xmax: 3417.538 ymax: 28376.68
Projected CRS: SVY21 / Singapore TM
PLN_AREA_N SUBZONE_N index TOTAL_TRIPS
1 TUAS TUAS VIEW EXTENSION 1 0
2 TUAS TUAS VIEW EXTENSION 2 0
3 TUAS TUAS VIEW EXTENSION 3 0
4 TUAS TUAS VIEW EXTENSION 4 0
5 TUAS TUAS VIEW EXTENSION 5 0
6 TUAS TUAS VIEW EXTENSION 6 0
geometry TRIPS_BIN
1 POLYGON ((2667.538 22314.5,... 0
2 POLYGON ((2667.538 23613.54... 0
3 POLYGON ((2667.538 24912.58... 0
4 POLYGON ((2667.538 26211.61... 0
5 POLYGON ((2667.538 27510.65... 0
6 POLYGON ((3042.538 21664.98... 0From the look of it, it appears that each hexagon has data on their respective planning area and subzone they belong to. This information will be useful when we want to create planning-area specific maps for inflow/outflow. We can simply filter our dataset to smaller, temporary data based on the user specification.
4.4.1 Planning Area Level Zooming
Firsly, let’s try creating inflow/outflow maps for planning area level. The user can specify a planning area, and we can filter the data accordingly before creating maps. We will create two functions, called inflow_pa_map and outflow_pa_map. Each function is designed to generate a specific type of map - inflow or outflow, respectively.
When a planning area name is provided as input to these functions, they will filter the dataset to only include data relevant to the specified area. Leveraging the tmap package, these functions will then create an interactive map. It’s important to note that these maps will maintain the same color palette and breaks as our previous overall maps, ensuring consistency in our visual representations.
inflow_pa_map <- function(pa_input) {
inflow_pa_temp <- inflow_data_weekday_morn_hex %>% filter(PLN_AREA_N == pa_input)
tmap_mode("view")
tm_shape(inflow_pa_temp) +
tm_fill(col = "TOTAL_TRIPS",
palette = c("#f2ffff","#f9f777","#f8d673","#f89974","#D66779","#b977cb","#7977f3","#57bfc0"),
style = "fixed",
breaks = c(0,1,100,1000,10000,100000,500000,1000000,5000000),
title = "Inflow Trip Count",
id= "TOTAL_TRIPS")+
tm_borders(col = "grey")
}outflow_pa_map <- function(pa_input) {
outflow_pa_temp <- outflow_data_weekday_morn_hex %>% filter(PLN_AREA_N == pa_input)
tmap_mode("view")
tm_shape(outflow_pa_temp) +
tm_fill(col = "TOTAL_TRIPS",
palette = c("#f2ffff","#f9f777","#f8d673","#f89974","#D66779","#b977cb","#7977f3","#57bfc0"),
style = "fixed",
breaks = c(0,1,100,1000,10000,100000,500000,1000000,5000000),
title = "Outflow Trip Count",
id= "TOTAL_TRIPS")+
tm_borders(col = "grey")
}As a demonstration, we call the inflow_pa_map() function with “HOUGANG” and the outflow_pa_map() function with “BUKIT PANJANG” as inputs. to test whether the functions works well and produce desired outcomes.
inflow_pa_map("HOUGANG")outflow_pa_map("BUKIT PANJANG")In the similar vein, we will also need to update our distribution graphs to specific planning area. To achieve that, we will create four functions below - inflow_pa_graph, outflow_pa_graph , inflow_pa_nozerograph and outflow_pa_nozerograph .
inflow_pa_graph <- function(pa_input) {
inflow_pa_temp <- inflow_data_weekday_morn_hex %>% filter(PLN_AREA_N == pa_input)
ggplot(data = inflow_pa_temp,
aes(y = TRIPS_BIN,fill = TRIPS_BIN)) +
geom_bar(show.legend = FALSE)+
xlab("Count of Analytical Hexagons") +
ylab("Inflow Trip Count") +
scale_fill_manual(values=color_map) +
ggtitle("Distribution of Hexagons Per Each Inflow Trip Count Bin")
}
outflow_pa_graph <- function(pa_input) {
outflow_pa_temp <- outflow_data_weekday_morn_hex %>% filter(PLN_AREA_N == pa_input)
ggplot(data = outflow_pa_temp,
aes(y = TRIPS_BIN,fill = TRIPS_BIN)) +
geom_bar(show.legend = FALSE)+
xlab("Count of Analytical Hexagons") +
ylab("Outflow Trip Count") +
scale_fill_manual(values=color_map) +
ggtitle("Distribution of Hexagons Per Each Outflow Trip Count Bin")
}
inflow_pa_nozerograph <- function(pa_input) {
inflow_pa_temp_nozero <- inflow_data_weekday_morn_hex %>% filter(PLN_AREA_N == pa_input, TOTAL_TRIPS != 0)
ggplot(data = inflow_pa_temp_nozero,
aes(y = TRIPS_BIN,fill = TRIPS_BIN)) +
geom_bar(show.legend = FALSE)+
xlab("Count of Analytical Hexagons") +
ylab("Inflow Trip Count") +
scale_fill_manual(values=color_map)+
ggtitle("Distribution of Hexagons Per Each Inflow Trip Count Bin",
subtitle = "(excluding hexagons with zero inflow trip)")
}
outflow_pa_nozerograph <- function(pa_input) {
outflow_pa_temp_nozero <- outflow_data_weekday_morn_hex %>% filter(PLN_AREA_N == pa_input, TOTAL_TRIPS != 0)
ggplot(data = outflow_pa_temp_nozero,
aes(y = TRIPS_BIN,fill = TRIPS_BIN)) +
geom_bar(show.legend = FALSE)+
xlab("Count of Analytical Hexagons") +
ylab("Outflow Trip Count") +
scale_fill_manual(values=color_map)+
ggtitle("Distribution of Hexagons Per Each Outflow Trip Count Bin",
subtitle = "(excluding hexagons with zero outflow trip)")
}As a demonstration, we call the inflow_pa_graph() & inflow_pa_nozerograph() functions with “HOUGANG” and the outflow_pa_graph() & outflow_pa_nozerograph() functions with “BUKIT PANJANG” as inputs to test whether the functions works well and produce desired outcomes.
inflow_pa_graph("HOUGANG")
inflow_pa_nozerograph("HOUGANG")
outflow_pa_graph("BUKIT PANJANG")
outflow_pa_nozerograph("BUKIT PANJANG")
4.4.2 Subzone Level Zooming
Similar to what we did with planning area level zooming, we can create functions for inflow/outflow maps at subzone level. Below, we have create two functions inflow_sz_map() and outflow_sz_map() using similar approach.
inflow_sz_map <- function(sz_input) {
inflow_sz_temp <- inflow_data_weekday_morn_hex %>% filter(SUBZONE_N == sz_input)
tmap_mode("view")
tm <- tm_shape(inflow_sz_temp) +
tm_fill(col = "TOTAL_TRIPS",
palette = c("#f2ffff","#f9f777","#f8d673","#f89974","#D66779","#b977cb","#7977f3","#57bfc0"),
style = "fixed",
breaks = c(0,1,100,1000,10000,100000,500000,1000000,5000000),
title = "Inflow Trip Count",
id= "TOTAL_TRIPS")+
tm_borders(col = "grey")
return(tm)
}outflow_sz_map <- function(sz_input) {
outflow_sz_temp <- outflow_data_weekday_morn_hex %>% filter(SUBZONE_N == sz_input)
tmap_mode("view")
tm <- tm_shape(outflow_sz_temp) +
tm_fill(col = "TOTAL_TRIPS",
palette = c("#f2ffff","#f9f777","#f8d673","#f89974","#D66779","#b977cb","#7977f3","#57bfc0"),
style = "fixed",
breaks = c(0,1,100,1000,10000,100000,500000,1000000,5000000),
title = "Outflow Trip Count",
id= "TOTAL_TRIPS")+
tm_borders(col = "grey")
return(tm)
}As a demonstration, we call the inflow_sz_map() function with “CHANGI AIRPORT” and the outflow_sz_map() function with “TUAS NORTH” as inputs to test whether the functions works well and produce desired outcomes.
inflow_sz_map("CHANGI AIRPORT")outflow_sz_map("TUAS NORTH")In the similar vein, we will also need to update our distribution graphs to specific subzone. To achieve that, we will create four functions below - inflow_sz_graph, outflow_sz_graph , inflow_sz_nozerograph and outflow_sz_nozerograph .
inflow_sz_graph <- function(sz_input) {
inflow_sz_temp <- inflow_data_weekday_morn_hex %>% filter(SUBZONE_N == sz_input)
ggplot(data = inflow_sz_temp,
aes(y = TRIPS_BIN,fill = TRIPS_BIN)) +
geom_bar(show.legend = FALSE)+
xlab("Count of Analytical Hexagons") +
ylab("Inflow Trip Count") +
scale_fill_manual(values=color_map) +
ggtitle("Distribution of Hexagons Per Each Inflow Trip Count Bin")
}
outflow_sz_graph <- function(sz_input) {
outflow_sz_temp <- outflow_data_weekday_morn_hex %>% filter(SUBZONE_N == sz_input)
ggplot(data = outflow_sz_temp,
aes(y = TRIPS_BIN,fill = TRIPS_BIN)) +
geom_bar(show.legend = FALSE)+
xlab("Count of Analytical Hexagons") +
ylab("Outflow Trip Count") +
scale_fill_manual(values=color_map) +
ggtitle("Distribution of Hexagons Per Each Outflow Trip Count Bin")
}
inflow_sz_nozerograph <- function(sz_input) {
inflow_sz_temp_nozero <- inflow_data_weekday_morn_hex %>% filter(SUBZONE_N == sz_input, TOTAL_TRIPS != 0)
ggplot(data = inflow_sz_temp_nozero,
aes(y = TRIPS_BIN,fill = TRIPS_BIN)) +
geom_bar(show.legend = FALSE)+
xlab("Count of Analytical Hexagons") +
ylab("Inflow Trip Count") +
scale_fill_manual(values=color_map)+
ggtitle("Distribution of Hexagons Per Each Inflow Trip Count Bin",
subtitle = "(excluding hexagons with zero inflow trip)")
}
outflow_sz_nozerograph <- function(sz_input) {
outflow_sz_temp_nozero <- outflow_data_weekday_morn_hex %>% filter(SUBZONE_N == sz_input, TOTAL_TRIPS != 0)
ggplot(data = outflow_sz_temp_nozero,
aes(y = TRIPS_BIN,fill = TRIPS_BIN)) +
geom_bar(show.legend = FALSE)+
xlab("Count of Analytical Hexagons") +
ylab("Outflow Trip Count") +
scale_fill_manual(values=color_map)+
ggtitle("Distribution of Hexagons Per Each Outflow Trip Count Bin",
subtitle = "(excluding hexagons with zero outflow trip)")
}As a demonstration, we call the inflow_sz_graph() & inflow_sz_nozerograph() functions with “CHANGI AIRPORT” and the outflow_sz_graph() & outflow_sz_nozerograph() functions with “TUAS NORTH” as inputs to test whether the functions works well and produce desired outcomes.
inflow_sz_graph("CHANGI AIRPORT")
inflow_sz_nozerograph("CHANGI AIRPORT")
outflow_sz_graph("TUAS NORTH")
outflow_sz_nozerograph("TUAS NORTH")
4.5 Exploring User Input Options for Shiny Application
From the exercise above, we may include the following user specification and model calibration options for our Shiny application.
| Input | Options |
|---|---|
| Flow Type | Incoming Flow, Outgoing Flow |
| Time Period | Weekday - Morning Peak , Weekday - Evening Peak, Weekend/Holiday - Morning Peak, Weekend/Holiday - Evening Peak |
| Zooming Level | Overall (Singapore) , Planning Area, Subzone |
| Area of Interest |
|
Reflection
Prototyping Thoughts
Initially, I had planned to use a slider for the time period, allowing users to specify the specific range of hours they wanted to examine. This seemed like the most viable approach. However, I soon realized that this could lead to heavy computation, especially if a user selected a very wide range (or possibly the entire dataset). This could potentially slow down our Shiny application, which would not be ideal for the user experience.
After some thought, I decided to switch to pre-determined time intervals, specifically focusing on morning and evening peak hours. While it’s still important to consider non-peak hours, I’ve noticed that most policy discussions around transport modeling tend to emphasize peak hours. Therefore, I believe it’s more useful and logical to focus on these peak periods.
For the morning peak, I plan to use the time from 6-8 AM, and for the evening peak, I intend to use 5-7 PM. This way, we can analyze the inflow and outflow patterns during the most critical hours of the day, providing valuable insights for transportation planning and policy making.
Below is a rough outline of how the user interface for this tabset might look like.
4.6 Spatial Interaction Modelling
In this section, we will test how we can implement and visualise spatial interaction modelling of origin-destination public bus flow data. In particular, we are planning to test using glm() functions from stats package to fit generalised linear models.
Applying log() Transformation to Explanatory Variables
Poisson regression is often used in spatial interaction modelling of origin-destination (OD) bus flow due to the nature of the data and the statistical properties of the Poisson distribution. Since Poisson Regression is based on log, log transformation of explanatory variables need to be done before running the model.
Hence, we apply log transformation to all columns in the flow dataset which ends with _count. These columns represent the explanatory variables of origin and destination hexagons in our dataset. We intuitively know that these variables need to be transformed because they are count data, which are often skewed and can benefit from a log transformation to meet the assumptions of Poisson regression. We also apply a log transformation to the dist column, which represents the distance between hexagons. This is done because distance is a continuous variable that can also be skewed and can benefit from a log transformation.
flow_data_weekday_morn_log <- flow_data_weekday_morn %>%
mutate_at(vars(ends_with("_count")), log) %>%
mutate(dist = log(dist))The transformed data is stored in a new data frame flow_data_weekday_morn_log. This data frame is now ready for Poisson regression analysis.
4.7 Origin (Production) Constrained Spatial Interaction Model
In this section, we will fit an origin constrained Spatial Interaction Model (SIM). For origin constrained SIM, only explanatory variables representing the attractiveness at the destinations will be used. This is because such models emphasize the limitations or capacities of the origins rather than the demand or attractiveness of the destinations. The capacity or limitation at the origin sites determines the potential for generating interactions or flows.
orcSIM_weekday_morn <- glm(TOTAL_TRIPS ~ ORIGIN_hex + d_biz_count + d_school_count + d_fin_count + d_hc_count + d_busstop_count + d_housing_count + d_leisure_recre_count + d_retail_count + d_entertn_count + d_food_bev_count + dist - 1,
family = poisson(link = "log"),
data = flow_data_weekday_morn_log,
na.action = na.exclude)In the formula argument, we specify our response variable TOTAL_TRIPS and our explanatory variables. The explanatory variables include ORIGIN_hex, various destination counts (e.g., d_biz_count, d_school_count, etc.), and dist. The -1 at the end of the formula is used to remove the intercept that is inserted by glm into the model by default. Since the origin has already been constrained, the concept of an intercept would not be relevant.
We will have a look at the results of the origin constrained spatial interaction model that we have just fitted.
orcSIM_weekday_morn
Call: glm(formula = TOTAL_TRIPS ~ ORIGIN_hex + d_biz_count + d_school_count +
d_fin_count + d_hc_count + d_busstop_count + d_housing_count +
d_leisure_recre_count + d_retail_count + d_entertn_count +
d_food_bev_count + dist - 1, family = poisson(link = "log"),
data = flow_data_weekday_morn_log, na.action = na.exclude)
Coefficients:
ORIGIN_hex29 ORIGIN_hex31 ORIGIN_hex39
13.941726 14.686527 14.511614
ORIGIN_hex40 ORIGIN_hex41 ORIGIN_hex49
15.778904 12.548848 15.481746
ORIGIN_hex50 ORIGIN_hex51 ORIGIN_hex52
14.448042 12.540246 15.580428
ORIGIN_hex59 ORIGIN_hex60 ORIGIN_hex61
16.418298 14.914117 15.570167
ORIGIN_hex62 ORIGIN_hex63 ORIGIN_hex72
14.939332 11.699034 13.298299
ORIGIN_hex73 ORIGIN_hex74 ORIGIN_hex75
12.827047 13.880245 13.115962
ORIGIN_hex83 ORIGIN_hex84 ORIGIN_hex85
15.843727 14.930012 14.157577
ORIGIN_hex86 ORIGIN_hex87 ORIGIN_hex88
12.878800 13.235495 13.713483
ORIGIN_hex89 ORIGIN_hex96 ORIGIN_hex97
14.333183 15.705128 13.478527
ORIGIN_hex99 ORIGIN_hex100 ORIGIN_hex101
15.656556 17.069264 17.633010
ORIGIN_hex112 ORIGIN_hex113 ORIGIN_hex114
12.712998 14.335755 9.490448
ORIGIN_hex124 ORIGIN_hex125 ORIGIN_hex126
11.158036 14.405082 12.649131
ORIGIN_hex135 ORIGIN_hex136 ORIGIN_hex137
13.751430 17.726486 15.109572
ORIGIN_hex145 ORIGIN_hex146 ORIGIN_hex147
14.442351 13.414143 14.671502
ORIGIN_hex155 ORIGIN_hex156 ORIGIN_hex157
12.901492 13.555591 12.787999
ORIGIN_hex168 ORIGIN_hex169 ORIGIN_hex170
13.614060 16.045080 13.388980
ORIGIN_hex181 ORIGIN_hex182 ORIGIN_hex183
14.431850 13.136444 16.318944
ORIGIN_hex197 ORIGIN_hex198 ORIGIN_hex199
13.374041 12.843618 15.123314
ORIGIN_hex213 ORIGIN_hex214 ORIGIN_hex215
14.133948 13.792650 13.679009
ORIGIN_hex231 ORIGIN_hex232 ORIGIN_hex233
11.864972 12.649000 13.923933
ORIGIN_hex249 ORIGIN_hex250 ORIGIN_hex252
14.318927 12.590541 13.560720
ORIGIN_hex265 ORIGIN_hex266 ORIGIN_hex267
15.251744 14.302182 18.523794
ORIGIN_hex268 ORIGIN_hex269 ORIGIN_hex283
14.848553 15.230772 12.871893
ORIGIN_hex284 ORIGIN_hex286 ORIGIN_hex287
14.823941 14.882120 14.957886
ORIGIN_hex300 ORIGIN_hex301 ORIGIN_hex302
14.685108 14.045611 14.496621
ORIGIN_hex303 ORIGIN_hex304 ORIGIN_hex319
17.099615 15.809899 14.844829
ORIGIN_hex320 ORIGIN_hex321 ORIGIN_hex322
15.050513 16.869942 14.963639
ORIGIN_hex323 ORIGIN_hex334 ORIGIN_hex335
12.706506 13.272007 14.371458
ORIGIN_hex336 ORIGIN_hex337 ORIGIN_hex339
14.782400 17.557906 14.237878
ORIGIN_hex340 ORIGIN_hex351 ORIGIN_hex352
15.203247 16.391398 13.927078
ORIGIN_hex353 ORIGIN_hex354 ORIGIN_hex355
16.592074 17.671888 15.454003
ORIGIN_hex356 ORIGIN_hex357 ORIGIN_hex367
11.976002 12.362910 15.152006
ORIGIN_hex368 ORIGIN_hex369 ORIGIN_hex370
14.709301 14.026531 18.372584
ORIGIN_hex371 ORIGIN_hex373 ORIGIN_hex374
18.027871 12.676713 11.958584
ORIGIN_hex375 ORIGIN_hex376 ORIGIN_hex377
13.566971 11.934741 13.742155
ORIGIN_hex385 ORIGIN_hex386 ORIGIN_hex387
10.686091 12.905636 14.193445
ORIGIN_hex388 ORIGIN_hex390 ORIGIN_hex393
17.644868 12.684819 14.400442
ORIGIN_hex394 ORIGIN_hex395 ORIGIN_hex402
15.097358 12.594786 14.357819
ORIGIN_hex403 ORIGIN_hex404 ORIGIN_hex405
14.228550 18.904142 16.998255
ORIGIN_hex407 ORIGIN_hex411 ORIGIN_hex412
10.682999 11.468764 12.235389
ORIGIN_hex413 ORIGIN_hex419 ORIGIN_hex420
16.169922 13.705286 15.350403
ORIGIN_hex421 ORIGIN_hex422 ORIGIN_hex424
13.784245 17.730347 11.862284
ORIGIN_hex430 ORIGIN_hex437 ORIGIN_hex438
13.092312 13.679218 15.626560
ORIGIN_hex439 ORIGIN_hex440 ORIGIN_hex442
16.397451 16.746905 14.310808
ORIGIN_hex453 ORIGIN_hex454 ORIGIN_hex455
13.896835 12.315058 14.040773
ORIGIN_hex456 ORIGIN_hex471 ORIGIN_hex472
17.900772 15.489828 16.898744
ORIGIN_hex473 ORIGIN_hex474 ORIGIN_hex476
16.760433 17.906871 16.957158
ORIGIN_hex487 ORIGIN_hex488 ORIGIN_hex489
15.443727 13.906721 17.307152
ORIGIN_hex490 ORIGIN_hex504 ORIGIN_hex505
16.132467 15.997330 17.133876
ORIGIN_hex506 ORIGIN_hex508 ORIGIN_hex518
17.509539 13.131467 14.877898
ORIGIN_hex521 ORIGIN_hex522 ORIGIN_hex524
16.657164 12.577267 13.372622
ORIGIN_hex533 ORIGIN_hex534 ORIGIN_hex536
13.631265 16.066051 16.532694
ORIGIN_hex537 ORIGIN_hex539 ORIGIN_hex549
17.006909 16.997830 17.316585
ORIGIN_hex550 ORIGIN_hex551 ORIGIN_hex552
17.211997 17.527378 17.243546
ORIGIN_hex554 ORIGIN_hex555 ORIGIN_hex559
18.379012 12.273256 12.981431
ORIGIN_hex562 ORIGIN_hex564 ORIGIN_hex565
13.758394 14.712020 16.454318
ORIGIN_hex566 ORIGIN_hex567 ORIGIN_hex568
17.085712 16.411728 18.284361
ORIGIN_hex569 ORIGIN_hex577 ORIGIN_hex579
16.586100 11.873080 16.322517
ORIGIN_hex580 ORIGIN_hex581 ORIGIN_hex582
17.091905 17.337976 17.214483
ORIGIN_hex583 ORIGIN_hex584 ORIGIN_hex585
16.227926 17.108052 17.942843
ORIGIN_hex586 ORIGIN_hex588 ORIGIN_hex589
16.458943 13.222997 14.602615
ORIGIN_hex593 ORIGIN_hex594 ORIGIN_hex595
13.996657 16.143341 15.492652
ORIGIN_hex596 ORIGIN_hex597 ORIGIN_hex598
17.705209 17.018654 17.850524
ORIGIN_hex599 ORIGIN_hex600 ORIGIN_hex601
17.493733 17.978466 17.434516
ORIGIN_hex603 ORIGIN_hex604 ORIGIN_hex609
13.538053 15.070148 14.075396
ORIGIN_hex610 ORIGIN_hex611 ORIGIN_hex612
14.375296 16.078312 14.962767
ORIGIN_hex613 ORIGIN_hex614 ORIGIN_hex615
16.483729 17.047782 16.759729
ORIGIN_hex616 ORIGIN_hex617 ORIGIN_hex618
17.726710 16.541255 18.493332
ORIGIN_hex619 ORIGIN_hex620 ORIGIN_hex625
14.119358 12.987757 13.520039
ORIGIN_hex626 ORIGIN_hex627 ORIGIN_hex628
15.440559 14.767378 16.005124
ORIGIN_hex629 ORIGIN_hex630 ORIGIN_hex631
18.196375 17.020451 16.004897
ORIGIN_hex632 ORIGIN_hex633 ORIGIN_hex634
16.176995 15.217277 15.002547
ORIGIN_hex635 ORIGIN_hex636 ORIGIN_hex643
13.438600 14.515111 16.469511
ORIGIN_hex644 ORIGIN_hex645 ORIGIN_hex646
16.461607 15.105560 17.751026
ORIGIN_hex649 ORIGIN_hex650 ORIGIN_hex651
16.889481 14.802467 16.281555
ORIGIN_hex652 ORIGIN_hex653 ORIGIN_hex654
14.087886 12.105089 12.745382
ORIGIN_hex659 ORIGIN_hex660 ORIGIN_hex661
16.314851 16.810256 15.060689
ORIGIN_hex662 ORIGIN_hex663 ORIGIN_hex665
16.094337 16.547124 15.315637
ORIGIN_hex666 ORIGIN_hex668 ORIGIN_hex669
17.295610 14.159800 16.718666
ORIGIN_hex670 ORIGIN_hex676 ORIGIN_hex677
15.898829 16.887221 16.928924
ORIGIN_hex678 ORIGIN_hex680 ORIGIN_hex681
17.290542 14.728050 17.129593
ORIGIN_hex682 ORIGIN_hex683 ORIGIN_hex687
15.744141 18.133636 18.494135
ORIGIN_hex688 ORIGIN_hex693 ORIGIN_hex694
15.390381 15.944302 17.741531
ORIGIN_hex695 ORIGIN_hex696 ORIGIN_hex697
18.829296 15.471369 16.258686
ORIGIN_hex698 ORIGIN_hex699 ORIGIN_hex700
14.840163 16.779738 16.824952
ORIGIN_hex701 ORIGIN_hex703 ORIGIN_hex706
17.904865 12.879872 19.579615
ORIGIN_hex711 ORIGIN_hex712 ORIGIN_hex713
15.085365 17.288895 16.110780
ORIGIN_hex715 ORIGIN_hex716 ORIGIN_hex718
16.791325 16.035828 17.205091
ORIGIN_hex722 ORIGIN_hex723 ORIGIN_hex729
16.422833 16.915723 15.749121
ORIGIN_hex730 ORIGIN_hex731 ORIGIN_hex732
11.246370 16.433882 15.708651
ORIGIN_hex733 ORIGIN_hex735 ORIGIN_hex736
17.056827 14.742062 18.322596
ORIGIN_hex737 ORIGIN_hex739 ORIGIN_hex741
17.500627 15.314887 18.058900
ORIGIN_hex742 ORIGIN_hex746 ORIGIN_hex747
17.639043 15.949597 14.222913
ORIGIN_hex748 ORIGIN_hex749 ORIGIN_hex750
17.243831 16.292277 15.314301
ORIGIN_hex751 ORIGIN_hex753 ORIGIN_hex754
16.011234 16.916974 15.869324
ORIGIN_hex758 ORIGIN_hex759 ORIGIN_hex760
16.185841 17.590699 13.796223
ORIGIN_hex764 ORIGIN_hex766 ORIGIN_hex767
17.558951 16.757200 15.802759
ORIGIN_hex769 ORIGIN_hex775 ORIGIN_hex777
16.134404 15.558900 17.145237
ORIGIN_hex778 ORIGIN_hex782 ORIGIN_hex783
17.457578 13.933052 16.234259
ORIGIN_hex784 ORIGIN_hex785 ORIGIN_hex786
17.206332 14.845523 18.094206
ORIGIN_hex794 ORIGIN_hex795 ORIGIN_hex796
14.694122 18.853688 18.207146
ORIGIN_hex799 ORIGIN_hex800 ORIGIN_hex801
16.082331 16.151337 14.860399
ORIGIN_hex802 ORIGIN_hex810 ORIGIN_hex812
15.348788 12.570259 17.661687
ORIGIN_hex813 ORIGIN_hex816 ORIGIN_hex817
16.923569 16.441912 15.711776
ORIGIN_hex818 ORIGIN_hex819 ORIGIN_hex820
14.263621 17.569668 14.997069
ORIGIN_hex821 ORIGIN_hex827 ORIGIN_hex829
15.841442 14.670104 15.720891
ORIGIN_hex830 ORIGIN_hex831 ORIGIN_hex835
17.667153 16.898253 15.088688
ORIGIN_hex836 ORIGIN_hex837 ORIGIN_hex838
16.142949 15.487210 15.747397
ORIGIN_hex847 ORIGIN_hex848 ORIGIN_hex849
17.735052 17.663137 15.130504
ORIGIN_hex851 ORIGIN_hex853 ORIGIN_hex854
15.361874 15.640549 15.580845
ORIGIN_hex856 ORIGIN_hex863 ORIGIN_hex864
16.526579 14.885474 15.370808
ORIGIN_hex865 ORIGIN_hex866 ORIGIN_hex867
18.493684 17.028145 8.989600
ORIGIN_hex868 ORIGIN_hex869 ORIGIN_hex870
14.269283 15.386265 16.608807
ORIGIN_hex871 ORIGIN_hex873 ORIGIN_hex882
17.590288 15.126386 18.014057
ORIGIN_hex883 ORIGIN_hex884 ORIGIN_hex885
17.725318 16.106893 12.387087
ORIGIN_hex887 ORIGIN_hex888 ORIGIN_hex889
15.871955 16.633082 15.969107
ORIGIN_hex890 ORIGIN_hex899 ORIGIN_hex901
15.906660 14.505301 17.346807
ORIGIN_hex902 ORIGIN_hex903 ORIGIN_hex905
17.112726 14.939543 17.017832
ORIGIN_hex906 ORIGIN_hex907 ORIGIN_hex909
16.329331 16.982982 16.597466
ORIGIN_hex910 ORIGIN_hex917 ORIGIN_hex920
15.983674 12.577237 17.731915
ORIGIN_hex922 ORIGIN_hex925 ORIGIN_hex926
14.252100 16.857232 16.566994
ORIGIN_hex927 ORIGIN_hex928 ORIGIN_hex929
16.302026 14.069325 15.766700
ORIGIN_hex936 ORIGIN_hex937 ORIGIN_hex940
14.942155 13.734781 16.754238
ORIGIN_hex941 ORIGIN_hex944 ORIGIN_hex945
15.962533 15.796854 16.576152
ORIGIN_hex946 ORIGIN_hex947 ORIGIN_hex949
16.268667 14.389526 15.294318
ORIGIN_hex955 ORIGIN_hex959 ORIGIN_hex960
13.321699 17.035019 17.439962
ORIGIN_hex962 ORIGIN_hex963 ORIGIN_hex964
14.217816 16.502438 16.799492
ORIGIN_hex965 ORIGIN_hex966 ORIGIN_hex968
17.610421 14.782014 16.303432
ORIGIN_hex969 ORIGIN_hex974 ORIGIN_hex975
12.981431 11.998804 16.190043
ORIGIN_hex978 ORIGIN_hex979 ORIGIN_hex980
15.040986 18.468961 16.290940
ORIGIN_hex983 ORIGIN_hex984 ORIGIN_hex985
17.399461 15.938544 15.296994
ORIGIN_hex986 ORIGIN_hex989 ORIGIN_hex993
15.823569 13.511580 12.576805
ORIGIN_hex994 ORIGIN_hex995 ORIGIN_hex996
17.525395 13.642925 12.447830
ORIGIN_hex998 ORIGIN_hex999 ORIGIN_hex1002
17.337974 16.835998 11.170660
ORIGIN_hex1004 ORIGIN_hex1005 ORIGIN_hex1006
17.257431 17.775195 14.798336
ORIGIN_hex1008 ORIGIN_hex1013 ORIGIN_hex1015
16.987636 15.591885 15.785615
ORIGIN_hex1016 ORIGIN_hex1017 ORIGIN_hex1018
14.053078 16.468865 16.531290
ORIGIN_hex1019 ORIGIN_hex1023 ORIGIN_hex1024
16.835881 15.561017 17.173393
ORIGIN_hex1025 ORIGIN_hex1026 ORIGIN_hex1027
16.471941 15.656089 15.712516
ORIGIN_hex1028 ORIGIN_hex1029 ORIGIN_hex1031
13.510506 11.737981 15.589593
ORIGIN_hex1032 ORIGIN_hex1034 ORIGIN_hex1035
16.238516 13.638489 13.265115
ORIGIN_hex1036 ORIGIN_hex1037 ORIGIN_hex1038
15.968548 18.327185 16.897474
ORIGIN_hex1039 ORIGIN_hex1044 ORIGIN_hex1045
14.388199 16.265022 16.307244
ORIGIN_hex1046 ORIGIN_hex1047 ORIGIN_hex1048
15.526123 15.357702 14.947427
ORIGIN_hex1051 ORIGIN_hex1052 ORIGIN_hex1053
16.537455 15.903160 15.486591
ORIGIN_hex1056 ORIGIN_hex1057 ORIGIN_hex1058
18.316466 16.990604 16.660822
ORIGIN_hex1059 ORIGIN_hex1063 ORIGIN_hex1065
17.925714 12.629304 14.115007
ORIGIN_hex1067 ORIGIN_hex1068 ORIGIN_hex1069
16.279083 15.267579 16.071086
ORIGIN_hex1070 ORIGIN_hex1071 ORIGIN_hex1072
16.404002 16.414358 16.890049
ORIGIN_hex1073 ORIGIN_hex1075 ORIGIN_hex1076
14.866919 15.282488 17.246158
ORIGIN_hex1077 ORIGIN_hex1078 ORIGIN_hex1079
17.860944 17.261760 16.045694
ORIGIN_hex1083 ORIGIN_hex1085 ORIGIN_hex1086
16.489408 15.455811 16.682858
ORIGIN_hex1088 ORIGIN_hex1089 ORIGIN_hex1090
15.200457 14.574898 16.175910
ORIGIN_hex1091 ORIGIN_hex1092 ORIGIN_hex1093
17.238538 17.511649 16.024937
ORIGIN_hex1095 ORIGIN_hex1096 ORIGIN_hex1097
18.051446 18.422598 17.190644
ORIGIN_hex1099 ORIGIN_hex1103 ORIGIN_hex1104
16.705139 14.469390 15.131660
ORIGIN_hex1106 ORIGIN_hex1107 ORIGIN_hex1108
16.332404 17.372863 16.618729
ORIGIN_hex1109 ORIGIN_hex1110 ORIGIN_hex1111
16.203701 16.634239 16.824714
ORIGIN_hex1112 ORIGIN_hex1115 ORIGIN_hex1116
16.590934 17.732854 18.821337
ORIGIN_hex1124 ORIGIN_hex1125 ORIGIN_hex1126
15.540055 16.520968 17.763893
ORIGIN_hex1127 ORIGIN_hex1128 ORIGIN_hex1129
15.016002 17.937846 17.547068
ORIGIN_hex1130 ORIGIN_hex1131 ORIGIN_hex1133
18.173383 14.674195 18.063239
ORIGIN_hex1134 ORIGIN_hex1142 ORIGIN_hex1143
18.325317 17.124013 16.151998
ORIGIN_hex1144 ORIGIN_hex1145 ORIGIN_hex1146
16.140934 16.932807 17.306902
ORIGIN_hex1147 ORIGIN_hex1148 ORIGIN_hex1149
16.943247 16.366466 14.153610
ORIGIN_hex1152 ORIGIN_hex1153 ORIGIN_hex1161
17.251356 17.515032 14.206411
ORIGIN_hex1162 ORIGIN_hex1163 ORIGIN_hex1164
16.985970 17.045217 17.021968
ORIGIN_hex1165 ORIGIN_hex1166 ORIGIN_hex1168
15.956534 18.039248 15.606248
ORIGIN_hex1171 ORIGIN_hex1178 ORIGIN_hex1179
18.000270 16.113331 16.410992
ORIGIN_hex1180 ORIGIN_hex1181 ORIGIN_hex1182
17.106675 16.758149 17.443294
ORIGIN_hex1183 ORIGIN_hex1187 ORIGIN_hex1194
17.388785 16.313968 14.005661
ORIGIN_hex1196 ORIGIN_hex1197 ORIGIN_hex1198
16.168565 18.444903 16.326346
ORIGIN_hex1199 ORIGIN_hex1200 ORIGIN_hex1202
14.308318 17.633565 16.255573
ORIGIN_hex1203 ORIGIN_hex1205 ORIGIN_hex1212
14.665980 15.769942 15.894448
ORIGIN_hex1213 ORIGIN_hex1214 ORIGIN_hex1215
17.140770 16.639706 15.651148
ORIGIN_hex1216 ORIGIN_hex1217 ORIGIN_hex1218
15.182060 15.083403 14.645178
ORIGIN_hex1220 ORIGIN_hex1221 ORIGIN_hex1226
12.190644 13.603521 15.321408
ORIGIN_hex1227 ORIGIN_hex1228 ORIGIN_hex1229
14.808829 17.737910 17.374194
ORIGIN_hex1230 ORIGIN_hex1231 ORIGIN_hex1232
15.021460 15.807932 15.938570
ORIGIN_hex1233 ORIGIN_hex1234 ORIGIN_hex1235
15.554207 14.264822 13.310347
ORIGIN_hex1236 ORIGIN_hex1243 ORIGIN_hex1244
12.019698 14.230935 17.622531
ORIGIN_hex1245 ORIGIN_hex1246 ORIGIN_hex1247
17.019429 16.791324 16.459718
ORIGIN_hex1248 ORIGIN_hex1249 ORIGIN_hex1251
14.874189 16.217108 13.660673
ORIGIN_hex1252 ORIGIN_hex1257 ORIGIN_hex1258
13.387452 16.705565 16.995316
ORIGIN_hex1259 ORIGIN_hex1260 ORIGIN_hex1261
16.346664 16.643829 15.831271
ORIGIN_hex1262 ORIGIN_hex1263 ORIGIN_hex1264
17.024770 17.312161 15.659703
ORIGIN_hex1265 ORIGIN_hex1266 ORIGIN_hex1267
17.436759 17.443253 15.152703
ORIGIN_hex1272 ORIGIN_hex1273 ORIGIN_hex1274
14.680517 15.989261 15.216407
ORIGIN_hex1275 ORIGIN_hex1276 ORIGIN_hex1277
15.702071 17.645803 16.498808
ORIGIN_hex1278 ORIGIN_hex1279 ORIGIN_hex1280
17.819289 16.530316 16.797529
ORIGIN_hex1281 ORIGIN_hex1285 ORIGIN_hex1286
12.843386 11.792834 16.577600
ORIGIN_hex1287 ORIGIN_hex1288 ORIGIN_hex1289
15.608486 16.730238 15.824725
ORIGIN_hex1290 ORIGIN_hex1291 ORIGIN_hex1292
15.828193 17.092593 17.237887
ORIGIN_hex1293 ORIGIN_hex1299 ORIGIN_hex1300
17.187038 16.272499 17.272346
ORIGIN_hex1301 ORIGIN_hex1302 ORIGIN_hex1303
16.023360 14.518261 16.467258
ORIGIN_hex1305 ORIGIN_hex1306 ORIGIN_hex1307
17.907382 17.816466 17.410182
ORIGIN_hex1312 ORIGIN_hex1313 ORIGIN_hex1314
16.298185 17.125249 15.896842
ORIGIN_hex1315 ORIGIN_hex1316 ORIGIN_hex1317
16.438264 14.549282 16.716732
ORIGIN_hex1318 ORIGIN_hex1319 ORIGIN_hex1320
17.026531 17.174566 17.677045
ORIGIN_hex1326 ORIGIN_hex1327 ORIGIN_hex1328
15.960319 16.789044 15.466883
ORIGIN_hex1329 ORIGIN_hex1330 ORIGIN_hex1331
17.280776 17.670690 17.275482
ORIGIN_hex1332 ORIGIN_hex1333 ORIGIN_hex1336
16.416664 17.170094 15.474541
ORIGIN_hex1337 ORIGIN_hex1338 ORIGIN_hex1339
16.378142 16.865610 15.104971
ORIGIN_hex1340 ORIGIN_hex1341 ORIGIN_hex1342
13.457586 16.646999 17.737851
ORIGIN_hex1343 ORIGIN_hex1344 ORIGIN_hex1345
16.989639 17.500813 18.077687
ORIGIN_hex1348 ORIGIN_hex1349 ORIGIN_hex1350
16.032886 16.507581 14.926218
ORIGIN_hex1351 ORIGIN_hex1352 ORIGIN_hex1353
14.689424 13.201876 17.409218
ORIGIN_hex1354 ORIGIN_hex1355 ORIGIN_hex1356
17.214238 17.631644 16.856051
ORIGIN_hex1357 ORIGIN_hex1359 ORIGIN_hex1360
17.009585 14.546477 16.645838
ORIGIN_hex1362 ORIGIN_hex1363 ORIGIN_hex1365
16.256283 14.137071 17.266998
ORIGIN_hex1366 ORIGIN_hex1367 ORIGIN_hex1368
16.875438 17.720569 18.070349
ORIGIN_hex1369 ORIGIN_hex1370 ORIGIN_hex1371
15.750391 16.507398 16.862575
ORIGIN_hex1372 ORIGIN_hex1373 ORIGIN_hex1374
17.475842 14.681814 15.317118
ORIGIN_hex1375 ORIGIN_hex1376 ORIGIN_hex1377
14.173151 17.198511 17.539748
ORIGIN_hex1378 ORIGIN_hex1379 ORIGIN_hex1382
17.992754 15.965411 16.112638
ORIGIN_hex1383 ORIGIN_hex1384 ORIGIN_hex1388
17.360037 16.447788 16.743708
ORIGIN_hex1389 ORIGIN_hex1390 ORIGIN_hex1391
18.617362 17.829950 16.962478
ORIGIN_hex1392 ORIGIN_hex1393 ORIGIN_hex1394
16.936814 16.444998 15.652475
ORIGIN_hex1395 ORIGIN_hex1397 ORIGIN_hex1399
14.115114 15.205715 17.034757
ORIGIN_hex1400 ORIGIN_hex1401 ORIGIN_hex1402
17.105069 14.646578 15.444933
ORIGIN_hex1404 ORIGIN_hex1405 ORIGIN_hex1406
16.227093 16.895880 17.652443
ORIGIN_hex1409 ORIGIN_hex1410 ORIGIN_hex1411
15.636668 11.433354 16.828489
ORIGIN_hex1412 ORIGIN_hex1413 ORIGIN_hex1414
17.122658 12.639092 16.673068
ORIGIN_hex1415 ORIGIN_hex1416 ORIGIN_hex1417
14.506310 16.400640 16.164204
ORIGIN_hex1420 ORIGIN_hex1422 ORIGIN_hex1426
11.291291 17.080428 16.122460
ORIGIN_hex1427 ORIGIN_hex1428 ORIGIN_hex1429
15.582142 16.538496 15.043929
ORIGIN_hex1432 ORIGIN_hex1433 ORIGIN_hex1434
12.998846 15.902035 17.530742
ORIGIN_hex1437 ORIGIN_hex1438 ORIGIN_hex1439
15.801557 17.502380 17.352608
ORIGIN_hex1442 ORIGIN_hex1444 ORIGIN_hex1446
16.287854 17.215700 16.356398
ORIGIN_hex1447 ORIGIN_hex1448 ORIGIN_hex1450
17.343619 17.375499 12.080689
ORIGIN_hex1451 ORIGIN_hex1456 ORIGIN_hex1457
14.117698 15.507512 17.558390
ORIGIN_hex1458 ORIGIN_hex1459 ORIGIN_hex1460
16.542813 17.608407 15.953953
ORIGIN_hex1461 ORIGIN_hex1465 ORIGIN_hex1466
16.488393 16.163076 17.322503
ORIGIN_hex1467 ORIGIN_hex1468 ORIGIN_hex1469
17.431679 16.680450 17.831600
ORIGIN_hex1470 ORIGIN_hex1471 ORIGIN_hex1475
16.606411 17.249899 16.309334
ORIGIN_hex1476 ORIGIN_hex1477 ORIGIN_hex1478
17.123746 16.120480 17.391347
ORIGIN_hex1479 ORIGIN_hex1480 ORIGIN_hex1481
17.359886 17.405422 15.159810
ORIGIN_hex1484 ORIGIN_hex1485 ORIGIN_hex1486
16.992488 17.214747 17.004646
ORIGIN_hex1487 ORIGIN_hex1488 ORIGIN_hex1489
17.388341 17.088861 17.399317
ORIGIN_hex1491 ORIGIN_hex1492 ORIGIN_hex1493
16.370831 17.454187 13.870729
ORIGIN_hex1494 ORIGIN_hex1495 ORIGIN_hex1496
18.094034 17.132408 17.966495
ORIGIN_hex1497 ORIGIN_hex1499 ORIGIN_hex1500
15.233620 17.240729 15.453620
ORIGIN_hex1501 ORIGIN_hex1502 ORIGIN_hex1503
16.077557 17.482216 15.834722
ORIGIN_hex1504 ORIGIN_hex1506 ORIGIN_hex1507
16.481122 16.046127 17.800950
ORIGIN_hex1508 ORIGIN_hex1509 ORIGIN_hex1510
16.698743 16.864839 16.553998
ORIGIN_hex1511 ORIGIN_hex1513 ORIGIN_hex1514
17.876134 14.019724 16.600677
ORIGIN_hex1515 ORIGIN_hex1516 ORIGIN_hex1517
15.336025 16.952507 17.437992
ORIGIN_hex1518 ORIGIN_hex1522 ORIGIN_hex1523
17.529659 15.642628 17.169452
ORIGIN_hex1524 ORIGIN_hex1525 ORIGIN_hex1528
17.093399 17.505508 16.436929
ORIGIN_hex1529 ORIGIN_hex1530 ORIGIN_hex1531
16.634541 17.518844 17.467879
ORIGIN_hex1532 ORIGIN_hex1534 ORIGIN_hex1535
17.675980 13.412019 16.040201
ORIGIN_hex1536 ORIGIN_hex1537 ORIGIN_hex1538
16.293275 17.041024 17.285379
ORIGIN_hex1540 ORIGIN_hex1541 ORIGIN_hex1542
13.999549 16.403323 17.484509
ORIGIN_hex1543 ORIGIN_hex1544 ORIGIN_hex1546
16.445268 17.040666 13.604972
ORIGIN_hex1547 ORIGIN_hex1548 ORIGIN_hex1549
12.548487 14.620608 15.333143
ORIGIN_hex1550 ORIGIN_hex1551 ORIGIN_hex1553
16.322607 13.821933 14.513254
ORIGIN_hex1554 ORIGIN_hex1555 ORIGIN_hex1556
15.959938 14.946524 15.219641
ORIGIN_hex1557 ORIGIN_hex1563 ORIGIN_hex1564
13.536711 15.066083 15.121793
ORIGIN_hex1565 ORIGIN_hex1570 ORIGIN_hex1571
14.600555 15.815852 13.526481
ORIGIN_hex1572 ORIGIN_hex1575 ORIGIN_hex1579
14.400076 17.271088 15.722251
ORIGIN_hex1583 ORIGIN_hex1584 ORIGIN_hex1587
15.684437 17.492428 16.070496
ORIGIN_hex1588 ORIGIN_hex1592 ORIGIN_hex1594
16.907067 16.901499 16.394029
ORIGIN_hex1602 ORIGIN_hex1603 ORIGIN_hex1608
12.497485 15.908894 16.867101
ORIGIN_hex1609 ORIGIN_hex1616 ORIGIN_hex1623
16.939043 15.914756 15.966861
ORIGIN_hex1630 ORIGIN_hex1643 ORIGIN_hex1644
11.262349 15.911123 17.598697
ORIGIN_hex1665 d_biz_count d_school_count
15.216507 0.134182 -0.223142
d_fin_count d_hc_count d_busstop_count
0.429166 0.007091 0.250849
d_housing_count d_leisure_recre_count d_retail_count
-0.043324 -0.015484 0.093737
d_entertn_count d_food_bev_count dist
0.211118 -0.272079 -1.561917
Degrees of Freedom: 51926 Total (i.e. Null); 51119 Residual
Null Deviance: 2.38e+08
Residual Deviance: 30360000 AIC: 306400004.8 Destination Constraint Spatial Interaction Model
Next, we will fit a destination constrained Spatial Interaction Model (SIM). For destination constrained SIM, only explanatory variables which represent how propulsive the origins are will be used. This is because such models emphasize the demand or attractiveness of the destinations rather than the limitations or capacities of the origins. The demand or attractiveness of the destination sites determines the potential for generating interactions or flows.
desSIM_weekday_morn <- glm(TOTAL_TRIPS ~ DESTIN_hex + o_biz_count + o_school_count + o_fin_count + o_hc_count + o_busstop_count + o_housing_count + o_leisure_recre_count + o_retail_count + o_entertn_count + o_food_bev_count + dist - 1,
family = poisson(link = "log"),
data = flow_data_weekday_morn_log,
na.action = na.exclude)desSIM_weekday_morn
Call: glm(formula = TOTAL_TRIPS ~ DESTIN_hex + o_biz_count + o_school_count +
o_fin_count + o_hc_count + o_busstop_count + o_housing_count +
o_leisure_recre_count + o_retail_count + o_entertn_count +
o_food_bev_count + dist - 1, family = poisson(link = "log"),
data = flow_data_weekday_morn_log, na.action = na.exclude)
Coefficients:
DESTIN_hex29 DESTIN_hex31 DESTIN_hex39
16.29641 16.92718 18.31263
DESTIN_hex40 DESTIN_hex41 DESTIN_hex49
18.14769 15.95552 14.98285
DESTIN_hex50 DESTIN_hex51 DESTIN_hex52
18.01659 17.28346 17.60414
DESTIN_hex59 DESTIN_hex60 DESTIN_hex61
16.38878 15.07300 16.40978
DESTIN_hex62 DESTIN_hex63 DESTIN_hex72
16.90342 15.57061 15.45554
DESTIN_hex73 DESTIN_hex74 DESTIN_hex75
17.76024 16.69284 16.14773
DESTIN_hex83 DESTIN_hex84 DESTIN_hex85
16.66879 16.57992 15.71083
DESTIN_hex86 DESTIN_hex87 DESTIN_hex88
16.36325 17.48318 17.30290
DESTIN_hex89 DESTIN_hex96 DESTIN_hex97
17.40281 14.56358 16.02026
DESTIN_hex99 DESTIN_hex100 DESTIN_hex101
17.63771 16.19638 16.21299
DESTIN_hex112 DESTIN_hex113 DESTIN_hex114
17.47549 15.96331 13.80291
DESTIN_hex124 DESTIN_hex125 DESTIN_hex126
14.95177 17.16265 15.54569
DESTIN_hex135 DESTIN_hex136 DESTIN_hex137
18.06108 16.07555 16.42547
DESTIN_hex145 DESTIN_hex146 DESTIN_hex147
15.32486 16.20131 17.24990
DESTIN_hex155 DESTIN_hex156 DESTIN_hex157
13.96431 15.99718 15.74272
DESTIN_hex168 DESTIN_hex169 DESTIN_hex170
17.10045 16.67306 16.43496
DESTIN_hex181 DESTIN_hex182 DESTIN_hex183
17.03828 16.21434 14.57910
DESTIN_hex197 DESTIN_hex198 DESTIN_hex199
16.87873 17.25488 18.09667
DESTIN_hex213 DESTIN_hex214 DESTIN_hex215
16.41227 17.18189 17.86791
DESTIN_hex231 DESTIN_hex232 DESTIN_hex233
14.49765 15.87206 18.75080
DESTIN_hex249 DESTIN_hex250 DESTIN_hex252
16.48458 17.25271 17.29257
DESTIN_hex265 DESTIN_hex266 DESTIN_hex267
17.25747 17.62888 16.95999
DESTIN_hex268 DESTIN_hex269 DESTIN_hex283
16.87531 17.92285 15.32062
DESTIN_hex284 DESTIN_hex286 DESTIN_hex287
17.50197 11.85000 16.19406
DESTIN_hex288 DESTIN_hex300 DESTIN_hex301
10.42242 16.44809 17.87703
DESTIN_hex302 DESTIN_hex303 DESTIN_hex304
16.92462 16.59241 16.03264
DESTIN_hex319 DESTIN_hex320 DESTIN_hex321
16.48005 16.06172 15.00611
DESTIN_hex322 DESTIN_hex323 DESTIN_hex334
18.51881 10.94554 15.09693
DESTIN_hex335 DESTIN_hex336 DESTIN_hex337
17.94818 16.17114 16.67617
DESTIN_hex339 DESTIN_hex340 DESTIN_hex351
15.50465 16.00509 17.40285
DESTIN_hex352 DESTIN_hex353 DESTIN_hex354
16.60806 16.56099 16.89379
DESTIN_hex355 DESTIN_hex356 DESTIN_hex357
15.07799 13.60477 13.40582
DESTIN_hex367 DESTIN_hex368 DESTIN_hex369
16.40754 16.14068 15.19648
DESTIN_hex370 DESTIN_hex371 DESTIN_hex373
17.44499 16.47690 14.33728
DESTIN_hex374 DESTIN_hex375 DESTIN_hex377
15.20796 15.70589 13.76290
DESTIN_hex385 DESTIN_hex386 DESTIN_hex387
17.91030 17.87884 17.99494
DESTIN_hex388 DESTIN_hex390 DESTIN_hex393
16.01277 14.83431 14.01670
DESTIN_hex394 DESTIN_hex395 DESTIN_hex402
15.85652 15.78621 17.02728
DESTIN_hex403 DESTIN_hex404 DESTIN_hex405
16.44295 18.16550 16.12394
DESTIN_hex407 DESTIN_hex411 DESTIN_hex412
13.39033 13.65494 14.69220
DESTIN_hex413 DESTIN_hex419 DESTIN_hex420
15.10991 15.34646 16.68797
DESTIN_hex421 DESTIN_hex422 DESTIN_hex424
16.93458 16.40840 11.62166
DESTIN_hex430 DESTIN_hex437 DESTIN_hex438
12.80808 15.14744 16.04508
DESTIN_hex439 DESTIN_hex440 DESTIN_hex442
15.72230 15.31732 16.12263
DESTIN_hex453 DESTIN_hex454 DESTIN_hex455
16.49762 14.00112 15.80098
DESTIN_hex456 DESTIN_hex471 DESTIN_hex472
17.93885 16.54571 16.84128
DESTIN_hex473 DESTIN_hex474 DESTIN_hex476
15.94792 17.06285 16.38364
DESTIN_hex487 DESTIN_hex488 DESTIN_hex489
17.25917 15.00148 16.83524
DESTIN_hex490 DESTIN_hex504 DESTIN_hex505
14.59170 15.39796 14.00833
DESTIN_hex506 DESTIN_hex508 DESTIN_hex518
16.56109 15.91734 16.01372
DESTIN_hex521 DESTIN_hex522 DESTIN_hex524
16.39886 14.07722 13.88928
DESTIN_hex533 DESTIN_hex534 DESTIN_hex536
17.31610 17.02287 16.33386
DESTIN_hex537 DESTIN_hex539 DESTIN_hex549
15.90306 14.82157 15.90941
DESTIN_hex550 DESTIN_hex551 DESTIN_hex552
16.49194 16.58595 16.39809
DESTIN_hex554 DESTIN_hex555 DESTIN_hex559
16.11706 13.44166 15.74426
DESTIN_hex562 DESTIN_hex564 DESTIN_hex565
16.17834 15.16197 15.52028
DESTIN_hex566 DESTIN_hex567 DESTIN_hex568
16.15829 14.87059 15.87050
DESTIN_hex569 DESTIN_hex577 DESTIN_hex579
14.96313 15.92645 16.11964
DESTIN_hex580 DESTIN_hex581 DESTIN_hex582
17.73335 16.16215 15.53380
DESTIN_hex583 DESTIN_hex584 DESTIN_hex585
13.56601 16.23676 16.16663
DESTIN_hex586 DESTIN_hex588 DESTIN_hex589
15.08426 16.28597 17.43083
DESTIN_hex593 DESTIN_hex594 DESTIN_hex595
14.99029 15.73119 17.00372
DESTIN_hex596 DESTIN_hex597 DESTIN_hex598
15.66153 16.63142 15.78979
DESTIN_hex599 DESTIN_hex600 DESTIN_hex601
16.13289 17.85474 17.71287
DESTIN_hex603 DESTIN_hex604 DESTIN_hex609
15.49592 15.92531 16.30754
DESTIN_hex610 DESTIN_hex611 DESTIN_hex612
17.15631 15.31163 16.72062
DESTIN_hex613 DESTIN_hex614 DESTIN_hex615
15.76358 17.42514 15.89984
DESTIN_hex616 DESTIN_hex617 DESTIN_hex618
16.60105 14.91042 15.66958
DESTIN_hex619 DESTIN_hex620 DESTIN_hex625
17.18331 16.35699 15.90081
DESTIN_hex626 DESTIN_hex627 DESTIN_hex628
15.89966 17.38338 17.72436
DESTIN_hex629 DESTIN_hex630 DESTIN_hex631
17.10516 14.46864 16.22649
DESTIN_hex632 DESTIN_hex633 DESTIN_hex634
14.10692 14.61651 17.40261
DESTIN_hex635 DESTIN_hex636 DESTIN_hex643
13.69972 16.03074 16.88169
DESTIN_hex644 DESTIN_hex645 DESTIN_hex646
14.97006 17.05999 16.66125
DESTIN_hex649 DESTIN_hex650 DESTIN_hex651
15.95821 14.51967 17.48656
DESTIN_hex652 DESTIN_hex653 DESTIN_hex654
14.21041 16.20476 15.64389
DESTIN_hex659 DESTIN_hex660 DESTIN_hex661
16.55934 16.15706 16.61647
DESTIN_hex662 DESTIN_hex663 DESTIN_hex665
17.94784 15.82993 14.13371
DESTIN_hex666 DESTIN_hex668 DESTIN_hex669
15.87139 14.15045 16.09034
DESTIN_hex670 DESTIN_hex676 DESTIN_hex677
13.70738 16.13062 15.30605
DESTIN_hex678 DESTIN_hex680 DESTIN_hex681
16.00508 14.81002 16.29755
DESTIN_hex682 DESTIN_hex683 DESTIN_hex687
16.23482 17.97632 19.11726
DESTIN_hex688 DESTIN_hex693 DESTIN_hex694
16.76484 15.92313 16.78572
DESTIN_hex695 DESTIN_hex696 DESTIN_hex697
18.14810 16.15677 15.96672
DESTIN_hex698 DESTIN_hex699 DESTIN_hex700
14.75713 17.34129 14.74735
DESTIN_hex701 DESTIN_hex703 DESTIN_hex706
15.91709 16.00450 18.41535
DESTIN_hex711 DESTIN_hex712 DESTIN_hex713
17.17691 16.33640 15.74858
DESTIN_hex715 DESTIN_hex716 DESTIN_hex718
16.28766 14.51063 15.74221
DESTIN_hex722 DESTIN_hex723 DESTIN_hex729
15.24229 15.83301 16.39729
DESTIN_hex730 DESTIN_hex731 DESTIN_hex732
16.37457 14.95630 18.38733
DESTIN_hex733 DESTIN_hex735 DESTIN_hex736
17.72282 16.12168 16.94901
DESTIN_hex737 DESTIN_hex739 DESTIN_hex741
15.19692 15.82299 17.55703
DESTIN_hex742 DESTIN_hex746 DESTIN_hex747
16.64277 17.37722 16.95057
DESTIN_hex748 DESTIN_hex749 DESTIN_hex750
16.79783 15.05996 17.90711
DESTIN_hex751 DESTIN_hex753 DESTIN_hex754
15.94297 15.35211 12.79231
DESTIN_hex758 DESTIN_hex759 DESTIN_hex760
15.50789 16.26208 12.99378
DESTIN_hex764 DESTIN_hex766 DESTIN_hex767
17.26778 16.61536 14.72141
DESTIN_hex769 DESTIN_hex775 DESTIN_hex777
16.42438 16.88471 15.95020
DESTIN_hex778 DESTIN_hex782 DESTIN_hex783
17.40000 16.97862 16.86281
DESTIN_hex784 DESTIN_hex785 DESTIN_hex786
15.71715 14.03997 15.42869
DESTIN_hex794 DESTIN_hex795 DESTIN_hex796
13.12554 18.66140 17.00230
DESTIN_hex799 DESTIN_hex800 DESTIN_hex801
15.34349 16.95155 14.97225
DESTIN_hex802 DESTIN_hex810 DESTIN_hex812
15.18772 13.59443 16.65419
DESTIN_hex813 DESTIN_hex816 DESTIN_hex817
16.41613 16.11271 16.34578
DESTIN_hex818 DESTIN_hex819 DESTIN_hex820
16.53949 17.25407 14.09708
DESTIN_hex821 DESTIN_hex827 DESTIN_hex829
16.02286 17.17713 16.66256
DESTIN_hex830 DESTIN_hex831 DESTIN_hex835
15.75598 18.25914 16.54881
DESTIN_hex836 DESTIN_hex837 DESTIN_hex838
14.86879 14.96897 14.93903
DESTIN_hex847 DESTIN_hex848 DESTIN_hex849
15.70374 16.02890 17.64578
DESTIN_hex851 DESTIN_hex853 DESTIN_hex854
17.53841 15.98112 15.48962
DESTIN_hex856 DESTIN_hex863 DESTIN_hex864
16.29192 15.61683 14.38210
DESTIN_hex865 DESTIN_hex866 DESTIN_hex867
17.77067 17.27811 16.33260
DESTIN_hex868 DESTIN_hex869 DESTIN_hex870
15.44363 15.76305 15.59238
DESTIN_hex871 DESTIN_hex873 DESTIN_hex882
17.10580 15.95062 16.75090
DESTIN_hex883 DESTIN_hex884 DESTIN_hex885
16.05142 17.45023 15.42082
DESTIN_hex887 DESTIN_hex888 DESTIN_hex889
17.62944 16.72057 15.38100
DESTIN_hex890 DESTIN_hex899 DESTIN_hex901
15.06131 14.75402 16.47535
DESTIN_hex902 DESTIN_hex903 DESTIN_hex905
16.82661 17.14287 16.09321
DESTIN_hex906 DESTIN_hex907 DESTIN_hex909
15.80358 16.21766 16.20054
DESTIN_hex910 DESTIN_hex917 DESTIN_hex920
15.45505 11.58802 16.20011
DESTIN_hex922 DESTIN_hex925 DESTIN_hex926
17.56027 15.46908 17.02325
DESTIN_hex927 DESTIN_hex928 DESTIN_hex929
15.20056 15.08114 15.70970
DESTIN_hex936 DESTIN_hex937 DESTIN_hex940
14.69043 15.51881 17.89282
DESTIN_hex941 DESTIN_hex944 DESTIN_hex945
17.46466 15.67584 17.17368
DESTIN_hex946 DESTIN_hex947 DESTIN_hex949
16.44105 14.78962 15.64079
DESTIN_hex955 DESTIN_hex959 DESTIN_hex960
12.88820 16.51514 15.74441
DESTIN_hex962 DESTIN_hex963 DESTIN_hex964
15.11301 16.20886 16.14377
DESTIN_hex965 DESTIN_hex966 DESTIN_hex968
17.05712 15.48857 16.59771
DESTIN_hex969 DESTIN_hex974 DESTIN_hex975
14.43042 11.88350 16.31805
DESTIN_hex978 DESTIN_hex979 DESTIN_hex980
15.55900 17.72151 15.94269
DESTIN_hex982 DESTIN_hex983 DESTIN_hex984
14.36549 17.27748 17.50656
DESTIN_hex985 DESTIN_hex986 DESTIN_hex989
15.19641 16.34563 13.05545
DESTIN_hex993 DESTIN_hex994 DESTIN_hex995
16.02937 16.57536 14.32543
DESTIN_hex996 DESTIN_hex998 DESTIN_hex999
14.90239 15.75031 15.30624
DESTIN_hex1002 DESTIN_hex1004 DESTIN_hex1005
16.32575 15.46392 17.11310
DESTIN_hex1006 DESTIN_hex1008 DESTIN_hex1013
14.30454 17.48354 17.58215
DESTIN_hex1015 DESTIN_hex1016 DESTIN_hex1017
15.70443 14.60192 15.19016
DESTIN_hex1018 DESTIN_hex1019 DESTIN_hex1023
15.70165 14.99829 15.52574
DESTIN_hex1024 DESTIN_hex1025 DESTIN_hex1026
15.55176 15.79976 16.02717
DESTIN_hex1027 DESTIN_hex1028 DESTIN_hex1029
15.99254 14.55928 11.79943
DESTIN_hex1031 DESTIN_hex1032 DESTIN_hex1034
15.23884 15.79969 13.38729
DESTIN_hex1035 DESTIN_hex1036 DESTIN_hex1037
13.65753 13.79952 17.32804
DESTIN_hex1038 DESTIN_hex1039 DESTIN_hex1044
17.26623 14.59677 15.30480
DESTIN_hex1045 DESTIN_hex1046 DESTIN_hex1047
15.68987 15.50631 14.66666
DESTIN_hex1048 DESTIN_hex1051 DESTIN_hex1052
15.58845 16.38789 14.56731
DESTIN_hex1053 DESTIN_hex1056 DESTIN_hex1057
14.94105 18.25204 15.46625
DESTIN_hex1058 DESTIN_hex1059 DESTIN_hex1063
15.59751 16.08979 11.94224
DESTIN_hex1065 DESTIN_hex1067 DESTIN_hex1068
13.97198 16.79921 16.11692
DESTIN_hex1069 DESTIN_hex1070 DESTIN_hex1071
15.86251 16.28662 16.57756
DESTIN_hex1072 DESTIN_hex1073 DESTIN_hex1075
16.45791 15.50890 13.31486
DESTIN_hex1076 DESTIN_hex1077 DESTIN_hex1078
16.47403 16.45026 15.09669
DESTIN_hex1079 DESTIN_hex1083 DESTIN_hex1085
14.27037 16.16364 16.24419
DESTIN_hex1086 DESTIN_hex1088 DESTIN_hex1089
16.86594 16.34920 14.77913
DESTIN_hex1090 DESTIN_hex1091 DESTIN_hex1092
15.56674 16.54548 16.03890
DESTIN_hex1093 DESTIN_hex1095 DESTIN_hex1096
14.97487 16.74975 18.51822
DESTIN_hex1097 DESTIN_hex1099 DESTIN_hex1103
16.78929 15.62976 17.05497
DESTIN_hex1104 DESTIN_hex1106 DESTIN_hex1107
15.80158 16.38075 16.89758
DESTIN_hex1108 DESTIN_hex1109 DESTIN_hex1110
15.58815 15.84993 16.14068
DESTIN_hex1111 DESTIN_hex1112 DESTIN_hex1115
14.57433 15.81470 16.05808
DESTIN_hex1116 DESTIN_hex1124 DESTIN_hex1125
17.16894 16.58038 16.75230
DESTIN_hex1126 DESTIN_hex1127 DESTIN_hex1128
17.99302 15.12216 16.00799
DESTIN_hex1129 DESTIN_hex1130 DESTIN_hex1131
16.43584 16.95588 17.06439
DESTIN_hex1133 DESTIN_hex1134 DESTIN_hex1142
15.66198 16.31346 17.04235
DESTIN_hex1143 DESTIN_hex1144 DESTIN_hex1145
16.33132 16.04894 16.56583
DESTIN_hex1146 DESTIN_hex1147 DESTIN_hex1148
17.95070 15.33209 17.16456
DESTIN_hex1149 DESTIN_hex1152 DESTIN_hex1153
17.22080 15.53158 15.23291
DESTIN_hex1161 DESTIN_hex1162 DESTIN_hex1163
15.68438 16.44650 16.59687
DESTIN_hex1164 DESTIN_hex1165 DESTIN_hex1166
15.89317 15.39079 17.66286
DESTIN_hex1168 DESTIN_hex1171 DESTIN_hex1178
17.74807 16.10481 14.84058
DESTIN_hex1179 DESTIN_hex1180 DESTIN_hex1181
15.41889 15.94268 15.65323
DESTIN_hex1182 DESTIN_hex1183 DESTIN_hex1187
16.64364 17.19725 14.46070
DESTIN_hex1194 DESTIN_hex1196 DESTIN_hex1197
17.10145 15.20870 16.76871
DESTIN_hex1198 DESTIN_hex1199 DESTIN_hex1200
16.34679 14.85885 16.13751
DESTIN_hex1202 DESTIN_hex1203 DESTIN_hex1205
15.09981 15.61749 13.14147
DESTIN_hex1212 DESTIN_hex1213 DESTIN_hex1214
16.44243 15.91963 15.20517
DESTIN_hex1215 DESTIN_hex1216 DESTIN_hex1217
15.20102 14.79757 16.09384
DESTIN_hex1218 DESTIN_hex1220 DESTIN_hex1221
12.02286 13.47387 15.67443
DESTIN_hex1226 DESTIN_hex1227 DESTIN_hex1228
16.24826 15.03495 16.81403
DESTIN_hex1229 DESTIN_hex1230 DESTIN_hex1231
17.27326 14.51452 14.90120
DESTIN_hex1232 DESTIN_hex1233 DESTIN_hex1234
16.84640 17.01107 14.64603
DESTIN_hex1235 DESTIN_hex1236 DESTIN_hex1243
15.15918 13.82568 17.08061
DESTIN_hex1244 DESTIN_hex1245 DESTIN_hex1246
17.59165 16.34658 16.66235
DESTIN_hex1247 DESTIN_hex1248 DESTIN_hex1249
15.99462 16.30521 15.66722
DESTIN_hex1251 DESTIN_hex1252 DESTIN_hex1257
14.73730 14.44512 15.79583
DESTIN_hex1258 DESTIN_hex1259 DESTIN_hex1260
16.66376 16.58094 15.00128
DESTIN_hex1261 DESTIN_hex1262 DESTIN_hex1263
14.66524 15.74632 17.05141
DESTIN_hex1264 DESTIN_hex1265 DESTIN_hex1266
16.88180 15.79559 16.57847
DESTIN_hex1267 DESTIN_hex1272 DESTIN_hex1273
14.38521 15.81062 16.56383
DESTIN_hex1274 DESTIN_hex1275 DESTIN_hex1276
17.27810 14.31424 17.89279
DESTIN_hex1277 DESTIN_hex1278 DESTIN_hex1279
15.20153 17.00334 14.12549
DESTIN_hex1280 DESTIN_hex1281 DESTIN_hex1285
15.40898 14.28952 14.10558
DESTIN_hex1286 DESTIN_hex1287 DESTIN_hex1288
16.52225 16.01219 16.75140
DESTIN_hex1289 DESTIN_hex1290 DESTIN_hex1291
15.65424 15.32052 15.92627
DESTIN_hex1292 DESTIN_hex1293 DESTIN_hex1299
15.56009 15.60191 15.48524
DESTIN_hex1300 DESTIN_hex1301 DESTIN_hex1302
16.74544 16.86256 16.48860
DESTIN_hex1303 DESTIN_hex1305 DESTIN_hex1306
15.35543 16.52008 15.78356
DESTIN_hex1307 DESTIN_hex1312 DESTIN_hex1313
14.22095 16.14640 16.75410
DESTIN_hex1314 DESTIN_hex1315 DESTIN_hex1316
15.84239 16.53437 14.27942
DESTIN_hex1317 DESTIN_hex1318 DESTIN_hex1319
17.77337 15.29781 16.21879
DESTIN_hex1320 DESTIN_hex1326 DESTIN_hex1327
15.41495 15.24032 16.86571
DESTIN_hex1328 DESTIN_hex1329 DESTIN_hex1330
16.76643 16.74141 15.34557
DESTIN_hex1331 DESTIN_hex1332 DESTIN_hex1333
16.39562 14.65960 14.94066
DESTIN_hex1336 DESTIN_hex1337 DESTIN_hex1338
15.69548 15.71988 16.73143
DESTIN_hex1339 DESTIN_hex1340 DESTIN_hex1341
17.69232 15.39858 16.36274
DESTIN_hex1342 DESTIN_hex1343 DESTIN_hex1344
17.63913 17.21034 17.01577
DESTIN_hex1345 DESTIN_hex1348 DESTIN_hex1349
15.31524 15.96773 17.31238
DESTIN_hex1350 DESTIN_hex1351 DESTIN_hex1352
17.41589 16.30721 16.64085
DESTIN_hex1353 DESTIN_hex1354 DESTIN_hex1355
16.35558 15.64513 15.39467
DESTIN_hex1356 DESTIN_hex1357 DESTIN_hex1359
15.78402 14.86682 14.63079
DESTIN_hex1360 DESTIN_hex1362 DESTIN_hex1363
15.55259 17.40801 17.45032
DESTIN_hex1365 DESTIN_hex1366 DESTIN_hex1367
15.07951 15.19568 17.28028
DESTIN_hex1368 DESTIN_hex1369 DESTIN_hex1370
16.28239 14.27554 16.72367
DESTIN_hex1371 DESTIN_hex1372 DESTIN_hex1373
17.09392 17.04130 16.26204
DESTIN_hex1374 DESTIN_hex1375 DESTIN_hex1376
15.19424 13.96590 14.82529
DESTIN_hex1377 DESTIN_hex1378 DESTIN_hex1379
15.70340 15.92395 14.07656
DESTIN_hex1382 DESTIN_hex1383 DESTIN_hex1384
15.93269 16.91798 16.97811
DESTIN_hex1388 DESTIN_hex1389 DESTIN_hex1390
14.76255 17.15438 17.41365
DESTIN_hex1391 DESTIN_hex1392 DESTIN_hex1393
14.89898 17.35480 15.96185
DESTIN_hex1394 DESTIN_hex1395 DESTIN_hex1397
13.39193 14.66296 16.69654
DESTIN_hex1399 DESTIN_hex1400 DESTIN_hex1401
15.23187 15.24989 14.73293
DESTIN_hex1402 DESTIN_hex1404 DESTIN_hex1405
15.49332 15.03993 16.75270
DESTIN_hex1406 DESTIN_hex1409 DESTIN_hex1410
17.23378 17.20002 13.30387
DESTIN_hex1411 DESTIN_hex1412 DESTIN_hex1413
16.47340 15.44817 11.49031
DESTIN_hex1414 DESTIN_hex1415 DESTIN_hex1416
16.06104 14.08950 15.83026
DESTIN_hex1417 DESTIN_hex1420 DESTIN_hex1422
16.10552 13.12173 15.03269
DESTIN_hex1426 DESTIN_hex1427 DESTIN_hex1428
15.78987 16.66740 16.63393
DESTIN_hex1429 DESTIN_hex1432 DESTIN_hex1433
15.04646 15.76927 14.62921
DESTIN_hex1434 DESTIN_hex1437 DESTIN_hex1438
14.85470 16.15605 16.26119
DESTIN_hex1439 DESTIN_hex1442 DESTIN_hex1444
16.15452 16.73256 14.81276
DESTIN_hex1446 DESTIN_hex1447 DESTIN_hex1448
15.95868 17.24665 15.90376
DESTIN_hex1450 DESTIN_hex1451 DESTIN_hex1456
13.21318 14.57710 15.52288
DESTIN_hex1457 DESTIN_hex1458 DESTIN_hex1459
17.58072 14.47280 16.38068
DESTIN_hex1460 DESTIN_hex1461 DESTIN_hex1465
15.45427 17.48512 15.60079
DESTIN_hex1466 DESTIN_hex1467 DESTIN_hex1468
17.13795 16.78346 17.32593
DESTIN_hex1469 DESTIN_hex1470 DESTIN_hex1471
16.08859 16.34632 17.40516
DESTIN_hex1475 DESTIN_hex1476 DESTIN_hex1477
15.76939 16.17682 15.29621
DESTIN_hex1478 DESTIN_hex1479 DESTIN_hex1480
16.22616 15.89087 15.95430
DESTIN_hex1481 DESTIN_hex1484 DESTIN_hex1485
14.18592 15.63891 15.89463
DESTIN_hex1486 DESTIN_hex1487 DESTIN_hex1488
17.16933 15.66301 14.56335
DESTIN_hex1489 DESTIN_hex1491 DESTIN_hex1492
16.22799 15.09935 16.14070
DESTIN_hex1493 DESTIN_hex1494 DESTIN_hex1495
15.13821 18.24505 15.46343
DESTIN_hex1496 DESTIN_hex1497 DESTIN_hex1499
15.88831 15.14075 15.43285
DESTIN_hex1500 DESTIN_hex1501 DESTIN_hex1502
15.09123 15.53684 17.18306
DESTIN_hex1503 DESTIN_hex1504 DESTIN_hex1506
14.05674 16.39559 15.49875
DESTIN_hex1507 DESTIN_hex1508 DESTIN_hex1509
17.63195 17.20760 15.17774
DESTIN_hex1510 DESTIN_hex1511 DESTIN_hex1513
15.17863 18.30008 15.61082
DESTIN_hex1514 DESTIN_hex1515 DESTIN_hex1516
15.66820 17.50274 16.39025
DESTIN_hex1517 DESTIN_hex1518 DESTIN_hex1522
17.30607 15.26933 14.48982
DESTIN_hex1523 DESTIN_hex1524 DESTIN_hex1525
15.90264 15.41000 16.08385
DESTIN_hex1528 DESTIN_hex1529 DESTIN_hex1530
16.50118 15.37757 16.42357
DESTIN_hex1531 DESTIN_hex1532 DESTIN_hex1534
16.30016 15.54965 15.24733
DESTIN_hex1535 DESTIN_hex1536 DESTIN_hex1537
16.96461 16.00129 15.66600
DESTIN_hex1538 DESTIN_hex1540 DESTIN_hex1541
15.73754 17.42169 15.70294
DESTIN_hex1542 DESTIN_hex1543 DESTIN_hex1544
16.03747 16.03281 15.28209
DESTIN_hex1546 DESTIN_hex1547 DESTIN_hex1548
17.78386 14.34794 17.48345
DESTIN_hex1549 DESTIN_hex1550 DESTIN_hex1551
14.65718 16.73587 15.56303
DESTIN_hex1553 DESTIN_hex1554 DESTIN_hex1555
17.24317 17.26108 15.75489
DESTIN_hex1556 DESTIN_hex1557 DESTIN_hex1563
15.07187 17.47967 14.87263
DESTIN_hex1564 DESTIN_hex1565 DESTIN_hex1570
15.55012 15.95036 16.12173
DESTIN_hex1571 DESTIN_hex1572 DESTIN_hex1575
14.82349 15.18867 17.44411
DESTIN_hex1579 DESTIN_hex1583 DESTIN_hex1584
15.53720 15.36478 17.88059
DESTIN_hex1587 DESTIN_hex1588 DESTIN_hex1592
16.07606 16.79744 18.16684
DESTIN_hex1594 DESTIN_hex1602 DESTIN_hex1603
15.59905 13.56039 15.93855
DESTIN_hex1608 DESTIN_hex1609 DESTIN_hex1616
18.23757 17.67051 16.72603
DESTIN_hex1623 DESTIN_hex1630 DESTIN_hex1643
17.58242 15.22870 13.21342
DESTIN_hex1644 DESTIN_hex1665 o_biz_count
17.94311 17.30459 -0.10419
o_school_count o_fin_count o_hc_count
0.01728 0.24959 0.01680
o_busstop_count o_housing_count o_leisure_recre_count
0.42481 0.11145 -0.04701
o_retail_count o_entertn_count o_food_bev_count
-0.05542 0.11920 0.03067
dist
-1.57648
Degrees of Freedom: 51926 Total (i.e. Null); 51118 Residual
Null Deviance: 2.38e+08
Residual Deviance: 28350000 AIC: 286200004.9 Doubly Constraint Spatial Interaction Model
In this section, we will fit a doubly constrained Spatial Interaction Model (SIM). For doubly constrained SIM, both the attractiveness at the destinations and the propulsiveness at the origins are considered. The model is typically expressed in the form of a distance function between the origin and destination.
dbcSIM_weekday_morn <- glm(formula = TOTAL_TRIPS ~
ORIGIN_hex +
DESTIN_hex +
dist,
family = poisson(link = "log"),
data = flow_data_weekday_morn_log,
na.action = na.exclude)In the formula argument, we specify our response variable TOTAL_TRIPS and our explanatory variables. The explanatory variables include ORIGIN_hex, DESTIN_hex, and dist.
dbcSIM_weekday_morn
Call: glm(formula = TOTAL_TRIPS ~ ORIGIN_hex + DESTIN_hex + dist, family = poisson(link = "log"),
data = flow_data_weekday_morn_log, na.action = na.exclude)
Coefficients:
(Intercept) ORIGIN_hex31 ORIGIN_hex39 ORIGIN_hex40 ORIGIN_hex41
13.616923 3.108157 1.282386 2.764515 -0.751642
ORIGIN_hex49 ORIGIN_hex50 ORIGIN_hex51 ORIGIN_hex52 ORIGIN_hex59
4.517471 2.119243 0.109137 3.183700 3.218399
ORIGIN_hex60 ORIGIN_hex61 ORIGIN_hex62 ORIGIN_hex63 ORIGIN_hex72
0.348340 2.585629 2.482757 -0.542673 0.866867
ORIGIN_hex73 ORIGIN_hex74 ORIGIN_hex75 ORIGIN_hex83 ORIGIN_hex84
0.510129 1.420133 1.437850 3.266378 2.489560
ORIGIN_hex85 ORIGIN_hex86 ORIGIN_hex87 ORIGIN_hex88 ORIGIN_hex89
1.309737 0.233333 1.498716 2.292051 2.794073
ORIGIN_hex96 ORIGIN_hex97 ORIGIN_hex99 ORIGIN_hex100 ORIGIN_hex101
3.993111 1.516809 4.051616 5.876286 6.245135
ORIGIN_hex112 ORIGIN_hex113 ORIGIN_hex114 ORIGIN_hex124 ORIGIN_hex125
1.825790 3.075366 -2.148361 -1.050485 3.154596
ORIGIN_hex126 ORIGIN_hex135 ORIGIN_hex136 ORIGIN_hex137 ORIGIN_hex145
1.085151 3.011202 6.560826 3.869734 3.021261
ORIGIN_hex146 ORIGIN_hex147 ORIGIN_hex155 ORIGIN_hex156 ORIGIN_hex157
1.320642 3.805546 1.006940 2.357705 1.549026
ORIGIN_hex168 ORIGIN_hex169 ORIGIN_hex170 ORIGIN_hex181 ORIGIN_hex182
1.622059 4.953055 2.146072 2.320082 1.339977
ORIGIN_hex183 ORIGIN_hex197 ORIGIN_hex198 ORIGIN_hex199 ORIGIN_hex213
5.278273 1.065849 1.541266 4.154037 1.778812
ORIGIN_hex214 ORIGIN_hex215 ORIGIN_hex231 ORIGIN_hex232 ORIGIN_hex233
1.885077 2.672229 0.563557 1.120968 2.437003
ORIGIN_hex249 ORIGIN_hex250 ORIGIN_hex252 ORIGIN_hex265 ORIGIN_hex266
2.503004 1.323100 1.225298 4.281566 2.575480
ORIGIN_hex267 ORIGIN_hex268 ORIGIN_hex269 ORIGIN_hex283 ORIGIN_hex284
7.297937 3.969403 3.420953 0.833831 3.480314
ORIGIN_hex286 ORIGIN_hex287 ORIGIN_hex300 ORIGIN_hex301 ORIGIN_hex302
2.571749 1.992990 2.601021 2.946429 3.501185
ORIGIN_hex303 ORIGIN_hex304 ORIGIN_hex319 ORIGIN_hex320 ORIGIN_hex321
6.302940 3.363259 3.937064 4.048172 5.509173
ORIGIN_hex322 ORIGIN_hex323 ORIGIN_hex334 ORIGIN_hex335 ORIGIN_hex336
3.093915 0.798616 0.360817 3.328856 3.573313
ORIGIN_hex337 ORIGIN_hex339 ORIGIN_hex340 ORIGIN_hex351 ORIGIN_hex352
6.347291 3.438284 5.051709 5.189642 2.141634
ORIGIN_hex353 ORIGIN_hex354 ORIGIN_hex355 ORIGIN_hex356 ORIGIN_hex357
5.475870 6.606664 2.855658 0.887057 0.852339
ORIGIN_hex367 ORIGIN_hex368 ORIGIN_hex369 ORIGIN_hex370 ORIGIN_hex371
2.349429 2.299380 3.004457 7.049873 6.500478
ORIGIN_hex373 ORIGIN_hex374 ORIGIN_hex375 ORIGIN_hex376 ORIGIN_hex377
1.456174 1.430720 3.141643 1.640500 2.437582
ORIGIN_hex385 ORIGIN_hex386 ORIGIN_hex387 ORIGIN_hex388 ORIGIN_hex390
-1.649634 1.565683 2.842534 6.211599 0.992620
ORIGIN_hex393 ORIGIN_hex394 ORIGIN_hex395 ORIGIN_hex402 ORIGIN_hex403
3.559711 4.982268 2.204878 2.232645 2.583991
ORIGIN_hex404 ORIGIN_hex405 ORIGIN_hex407 ORIGIN_hex411 ORIGIN_hex412
7.804138 5.784762 -0.700720 1.524585 2.083496
ORIGIN_hex413 ORIGIN_hex419 ORIGIN_hex420 ORIGIN_hex421 ORIGIN_hex422
5.297753 2.422578 3.409557 2.423697 6.340159
ORIGIN_hex424 ORIGIN_hex430 ORIGIN_hex437 ORIGIN_hex438 ORIGIN_hex439
0.676274 2.068597 2.158178 4.259282 4.965663
ORIGIN_hex440 ORIGIN_hex442 ORIGIN_hex453 ORIGIN_hex454 ORIGIN_hex455
5.488988 3.424790 2.563508 1.031783 2.994377
ORIGIN_hex456 ORIGIN_hex471 ORIGIN_hex472 ORIGIN_hex473 ORIGIN_hex474
7.074776 4.218739 6.079784 5.711551 6.801711
ORIGIN_hex476 ORIGIN_hex487 ORIGIN_hex488 ORIGIN_hex489 ORIGIN_hex490
6.396342 4.594346 2.807507 6.352599 4.941993
ORIGIN_hex504 ORIGIN_hex505 ORIGIN_hex506 ORIGIN_hex508 ORIGIN_hex518
5.122761 5.919770 6.611424 2.386124 3.372878
ORIGIN_hex521 ORIGIN_hex522 ORIGIN_hex524 ORIGIN_hex533 ORIGIN_hex534
5.743532 2.026695 2.640870 2.533237 4.904280
ORIGIN_hex536 ORIGIN_hex537 ORIGIN_hex539 ORIGIN_hex549 ORIGIN_hex550
5.754481 6.114337 6.396797 6.324043 6.150883
ORIGIN_hex551 ORIGIN_hex552 ORIGIN_hex554 ORIGIN_hex555 ORIGIN_hex559
6.645373 6.435831 7.936206 1.621963 2.204942
ORIGIN_hex562 ORIGIN_hex564 ORIGIN_hex565 ORIGIN_hex566 ORIGIN_hex567
2.294885 3.782419 5.497732 6.237086 5.497976
ORIGIN_hex568 ORIGIN_hex569 ORIGIN_hex577 ORIGIN_hex579 ORIGIN_hex580
7.731980 5.644009 0.805500 5.239358 6.070136
ORIGIN_hex581 ORIGIN_hex582 ORIGIN_hex583 ORIGIN_hex584 ORIGIN_hex585
6.460469 6.399364 5.484094 6.315175 7.110345
ORIGIN_hex586 ORIGIN_hex588 ORIGIN_hex589 ORIGIN_hex593 ORIGIN_hex594
5.707877 2.015736 3.851516 2.602769 5.181994
ORIGIN_hex595 ORIGIN_hex596 ORIGIN_hex597 ORIGIN_hex598 ORIGIN_hex599
4.401954 6.471517 6.110269 6.967940 6.782857
ORIGIN_hex600 ORIGIN_hex601 ORIGIN_hex603 ORIGIN_hex604 ORIGIN_hex609
7.417486 6.762482 2.133127 4.377790 2.816489
ORIGIN_hex610 ORIGIN_hex611 ORIGIN_hex612 ORIGIN_hex613 ORIGIN_hex614
2.970151 4.986625 3.634936 5.399528 6.177346
ORIGIN_hex615 ORIGIN_hex616 ORIGIN_hex617 ORIGIN_hex618 ORIGIN_hex619
5.916952 6.817746 5.468504 7.716098 2.864944
ORIGIN_hex620 ORIGIN_hex625 ORIGIN_hex626 ORIGIN_hex627 ORIGIN_hex628
2.142215 2.233070 4.233454 3.411942 4.608153
ORIGIN_hex629 ORIGIN_hex630 ORIGIN_hex631 ORIGIN_hex632 ORIGIN_hex633
7.198236 6.242075 5.170560 5.090560 3.910853
ORIGIN_hex634 ORIGIN_hex635 ORIGIN_hex636 ORIGIN_hex643 ORIGIN_hex644
3.708353 1.943813 3.088617 5.154151 5.078427
ORIGIN_hex645 ORIGIN_hex646 ORIGIN_hex649 ORIGIN_hex650 ORIGIN_hex651
3.612085 6.502796 6.011781 3.679306 5.107627
ORIGIN_hex652 ORIGIN_hex653 ORIGIN_hex654 ORIGIN_hex659 ORIGIN_hex660
2.525633 1.355156 1.549869 4.844835 5.289456
ORIGIN_hex661 ORIGIN_hex662 ORIGIN_hex663 ORIGIN_hex665 ORIGIN_hex666
3.610826 4.915898 5.579789 4.254335 6.295522
ORIGIN_hex668 ORIGIN_hex669 ORIGIN_hex670 ORIGIN_hex676 ORIGIN_hex677
2.315667 4.942607 3.506751 5.605513 5.468181
ORIGIN_hex678 ORIGIN_hex680 ORIGIN_hex681 ORIGIN_hex682 ORIGIN_hex683
5.657116 3.755243 6.142685 4.724671 7.395829
ORIGIN_hex687 ORIGIN_hex688 ORIGIN_hex693 ORIGIN_hex694 ORIGIN_hex695
7.484405 3.021750 4.450179 6.287707 7.603166
ORIGIN_hex696 ORIGIN_hex697 ORIGIN_hex698 ORIGIN_hex699 ORIGIN_hex700
3.533237 4.774685 3.799294 5.859449 5.768208
ORIGIN_hex701 ORIGIN_hex703 ORIGIN_hex706 ORIGIN_hex711 ORIGIN_hex712
7.001605 1.494280 8.472036 3.522311 5.794016
ORIGIN_hex713 ORIGIN_hex715 ORIGIN_hex716 ORIGIN_hex718 ORIGIN_hex722
4.331849 5.530903 4.913303 6.155446 5.020036
ORIGIN_hex723 ORIGIN_hex729 ORIGIN_hex730 ORIGIN_hex731 ORIGIN_hex732
5.154208 4.249488 -0.676706 4.791285 4.313797
ORIGIN_hex733 ORIGIN_hex735 ORIGIN_hex736 ORIGIN_hex737 ORIGIN_hex739
5.737168 3.652904 7.470399 6.748144 3.643431
ORIGIN_hex741 ORIGIN_hex742 ORIGIN_hex746 ORIGIN_hex747 ORIGIN_hex748
6.564464 5.719904 4.277217 2.809785 5.767287
ORIGIN_hex749 ORIGIN_hex750 ORIGIN_hex751 ORIGIN_hex753 ORIGIN_hex754
4.576561 3.697110 4.840363 5.808926 5.356103
ORIGIN_hex758 ORIGIN_hex759 ORIGIN_hex760 ORIGIN_hex764 ORIGIN_hex766
4.812751 5.777508 2.167080 6.112824 5.353553
ORIGIN_hex767 ORIGIN_hex769 ORIGIN_hex775 ORIGIN_hex777 ORIGIN_hex778
4.693406 4.654197 3.987131 5.543328 5.024799
ORIGIN_hex782 ORIGIN_hex783 ORIGIN_hex784 ORIGIN_hex785 ORIGIN_hex786
2.168065 4.764671 5.856641 3.414738 6.634781
ORIGIN_hex794 ORIGIN_hex795 ORIGIN_hex796 ORIGIN_hex799 ORIGIN_hex800
2.810848 7.837061 6.321947 4.423156 4.556793
ORIGIN_hex801 ORIGIN_hex802 ORIGIN_hex810 ORIGIN_hex812 ORIGIN_hex813
3.397677 4.069969 0.006596 5.809800 4.718843
ORIGIN_hex816 ORIGIN_hex817 ORIGIN_hex818 ORIGIN_hex819 ORIGIN_hex820
4.675665 4.371035 2.823024 6.355046 4.110540
ORIGIN_hex821 ORIGIN_hex827 ORIGIN_hex829 ORIGIN_hex830 ORIGIN_hex831
4.665753 3.011651 4.472325 5.992520 5.154307
ORIGIN_hex835 ORIGIN_hex836 ORIGIN_hex837 ORIGIN_hex838 ORIGIN_hex847
3.609314 4.812077 4.295062 4.722881 6.141961
ORIGIN_hex848 ORIGIN_hex849 ORIGIN_hex851 ORIGIN_hex853 ORIGIN_hex854
6.046644 3.433145 3.667767 4.332216 4.224064
ORIGIN_hex856 ORIGIN_hex863 ORIGIN_hex864 ORIGIN_hex865 ORIGIN_hex866
5.409492 3.279049 3.930718 7.203848 5.597089
ORIGIN_hex867 ORIGIN_hex868 ORIGIN_hex869 ORIGIN_hex870 ORIGIN_hex871
-2.412780 2.330203 3.712496 5.249502 6.539811
ORIGIN_hex873 ORIGIN_hex882 ORIGIN_hex883 ORIGIN_hex884 ORIGIN_hex885
4.044716 6.697557 6.139965 4.549370 1.088550
ORIGIN_hex887 ORIGIN_hex888 ORIGIN_hex889 ORIGIN_hex890 ORIGIN_hex899
4.336156 5.212590 4.628424 4.638126 3.311433
ORIGIN_hex901 ORIGIN_hex902 ORIGIN_hex903 ORIGIN_hex905 ORIGIN_hex906
5.901097 5.543477 3.357407 5.347449 4.608512
ORIGIN_hex907 ORIGIN_hex909 ORIGIN_hex910 ORIGIN_hex917 ORIGIN_hex920
5.599818 5.496417 4.832996 1.712665 6.300146
ORIGIN_hex922 ORIGIN_hex925 ORIGIN_hex926 ORIGIN_hex927 ORIGIN_hex928
2.824797 5.054287 5.194211 5.032163 2.874891
ORIGIN_hex929 ORIGIN_hex936 ORIGIN_hex937 ORIGIN_hex940 ORIGIN_hex941
4.564464 3.667964 2.863301 5.264751 4.598075
ORIGIN_hex944 ORIGIN_hex945 ORIGIN_hex946 ORIGIN_hex947 ORIGIN_hex949
4.127775 5.042834 4.904495 3.245281 4.255790
ORIGIN_hex955 ORIGIN_hex959 ORIGIN_hex960 ORIGIN_hex962 ORIGIN_hex963
2.492899 5.806873 6.090583 2.587150 5.030036
ORIGIN_hex964 ORIGIN_hex965 ORIGIN_hex966 ORIGIN_hex968 ORIGIN_hex969
5.094024 6.076668 3.568290 4.882531 1.889541
ORIGIN_hex974 ORIGIN_hex975 ORIGIN_hex978 ORIGIN_hex979 ORIGIN_hex980
0.277375 5.157647 3.599007 7.311119 4.913297
ORIGIN_hex983 ORIGIN_hex984 ORIGIN_hex985 ORIGIN_hex986 ORIGIN_hex989
6.092696 4.561877 4.001677 4.602953 2.429395
ORIGIN_hex993 ORIGIN_hex994 ORIGIN_hex995 ORIGIN_hex996 ORIGIN_hex998
0.896046 6.747206 2.801903 1.715330 6.128571
ORIGIN_hex999 ORIGIN_hex1002 ORIGIN_hex1004 ORIGIN_hex1005 ORIGIN_hex1006
5.581576 0.453172 5.602553 6.476839 3.797241
ORIGIN_hex1008 ORIGIN_hex1013 ORIGIN_hex1015 ORIGIN_hex1016 ORIGIN_hex1017
5.885483 4.739547 4.532675 3.121235 5.447631
ORIGIN_hex1018 ORIGIN_hex1019 ORIGIN_hex1023 ORIGIN_hex1024 ORIGIN_hex1025
5.207965 5.636500 3.988803 5.673004 5.209754
ORIGIN_hex1026 ORIGIN_hex1027 ORIGIN_hex1028 ORIGIN_hex1029 ORIGIN_hex1031
4.521470 4.284296 1.721053 0.219987 4.630951
ORIGIN_hex1032 ORIGIN_hex1034 ORIGIN_hex1035 ORIGIN_hex1036 ORIGIN_hex1037
5.003078 2.867719 1.572434 4.993633 7.352428
ORIGIN_hex1038 ORIGIN_hex1039 ORIGIN_hex1044 ORIGIN_hex1045 ORIGIN_hex1046
5.975796 3.043416 4.834171 5.088752 4.516462
ORIGIN_hex1047 ORIGIN_hex1048 ORIGIN_hex1051 ORIGIN_hex1052 ORIGIN_hex1053
3.916671 3.674640 5.373200 4.765551 4.264612
ORIGIN_hex1056 ORIGIN_hex1057 ORIGIN_hex1058 ORIGIN_hex1059 ORIGIN_hex1063
7.485690 5.747987 5.554830 6.873288 1.076369
ORIGIN_hex1065 ORIGIN_hex1067 ORIGIN_hex1068 ORIGIN_hex1069 ORIGIN_hex1070
2.684223 4.944552 3.896049 4.925303 5.368740
ORIGIN_hex1071 ORIGIN_hex1072 ORIGIN_hex1073 ORIGIN_hex1075 ORIGIN_hex1076
5.319544 5.832816 3.654284 3.749801 6.009215
ORIGIN_hex1077 ORIGIN_hex1078 ORIGIN_hex1079 ORIGIN_hex1083 ORIGIN_hex1085
6.730801 5.890375 4.810417 5.184913 4.400650
ORIGIN_hex1086 ORIGIN_hex1088 ORIGIN_hex1089 ORIGIN_hex1090 ORIGIN_hex1091
5.527132 3.800116 3.399453 5.018021 6.105192
ORIGIN_hex1092 ORIGIN_hex1093 ORIGIN_hex1095 ORIGIN_hex1096 ORIGIN_hex1097
6.157005 4.648733 6.744666 7.580549 6.135281
ORIGIN_hex1099 ORIGIN_hex1103 ORIGIN_hex1104 ORIGIN_hex1106 ORIGIN_hex1107
6.103983 3.230693 4.232010 5.230622 6.095340
ORIGIN_hex1108 ORIGIN_hex1109 ORIGIN_hex1110 ORIGIN_hex1111 ORIGIN_hex1112
5.280077 4.946745 5.478459 5.395796 5.257270
ORIGIN_hex1115 ORIGIN_hex1116 ORIGIN_hex1124 ORIGIN_hex1125 ORIGIN_hex1126
6.602856 7.742905 4.186497 5.306018 6.712183
ORIGIN_hex1127 ORIGIN_hex1128 ORIGIN_hex1129 ORIGIN_hex1130 ORIGIN_hex1131
3.799982 6.635490 6.276757 6.940560 3.168224
ORIGIN_hex1133 ORIGIN_hex1134 ORIGIN_hex1142 ORIGIN_hex1143 ORIGIN_hex1144
7.095715 7.176635 6.051460 5.088259 4.684013
ORIGIN_hex1145 ORIGIN_hex1146 ORIGIN_hex1147 ORIGIN_hex1148 ORIGIN_hex1149
5.637105 6.211563 5.469014 4.917357 2.431127
ORIGIN_hex1152 ORIGIN_hex1153 ORIGIN_hex1161 ORIGIN_hex1162 ORIGIN_hex1163
6.291306 6.412164 3.256668 5.778929 5.663600
ORIGIN_hex1164 ORIGIN_hex1165 ORIGIN_hex1166 ORIGIN_hex1168 ORIGIN_hex1171
5.809170 4.683536 6.895264 4.267033 7.201534
ORIGIN_hex1178 ORIGIN_hex1179 ORIGIN_hex1180 ORIGIN_hex1181 ORIGIN_hex1182
4.933274 5.124088 5.940962 5.432343 6.158984
ORIGIN_hex1183 ORIGIN_hex1187 ORIGIN_hex1194 ORIGIN_hex1196 ORIGIN_hex1197
5.934290 5.277965 2.831195 4.618703 7.387951
ORIGIN_hex1198 ORIGIN_hex1199 ORIGIN_hex1200 ORIGIN_hex1202 ORIGIN_hex1203
5.155471 2.882618 6.273532 4.802661 3.855351
ORIGIN_hex1205 ORIGIN_hex1212 ORIGIN_hex1213 ORIGIN_hex1214 ORIGIN_hex1215
4.918812 4.736029 5.822503 5.289567 4.395017
ORIGIN_hex1216 ORIGIN_hex1217 ORIGIN_hex1218 ORIGIN_hex1220 ORIGIN_hex1221
4.188166 3.650315 3.045945 1.292917 2.992053
ORIGIN_hex1226 ORIGIN_hex1227 ORIGIN_hex1228 ORIGIN_hex1229 ORIGIN_hex1230
4.205201 3.533404 6.442040 5.619445 3.671046
ORIGIN_hex1231 ORIGIN_hex1232 ORIGIN_hex1233 ORIGIN_hex1234 ORIGIN_hex1235
4.672352 4.754175 4.304192 3.136180 2.465481
ORIGIN_hex1236 ORIGIN_hex1243 ORIGIN_hex1244 ORIGIN_hex1245 ORIGIN_hex1246
1.363680 2.876792 6.339869 5.848773 5.611092
ORIGIN_hex1247 ORIGIN_hex1248 ORIGIN_hex1249 ORIGIN_hex1251 ORIGIN_hex1252
5.286027 3.532790 5.047053 2.972384 2.501188
ORIGIN_hex1257 ORIGIN_hex1258 ORIGIN_hex1259 ORIGIN_hex1260 ORIGIN_hex1261
5.694904 5.911076 4.779099 5.216067 4.526783
ORIGIN_hex1262 ORIGIN_hex1263 ORIGIN_hex1264 ORIGIN_hex1265 ORIGIN_hex1266
5.835086 6.229764 4.413197 6.519695 6.712137
ORIGIN_hex1267 ORIGIN_hex1272 ORIGIN_hex1273 ORIGIN_hex1274 ORIGIN_hex1275
4.602652 3.405355 4.661204 3.838529 4.533025
ORIGIN_hex1276 ORIGIN_hex1277 ORIGIN_hex1278 ORIGIN_hex1279 ORIGIN_hex1280
6.622510 5.406593 6.634957 5.418719 6.000338
ORIGIN_hex1281 ORIGIN_hex1285 ORIGIN_hex1286 ORIGIN_hex1287 ORIGIN_hex1288
2.057143 0.674091 5.415655 4.320850 5.474090
ORIGIN_hex1289 ORIGIN_hex1290 ORIGIN_hex1291 ORIGIN_hex1292 ORIGIN_hex1293
4.577832 4.726606 5.982332 6.107349 6.317009
ORIGIN_hex1299 ORIGIN_hex1300 ORIGIN_hex1301 ORIGIN_hex1302 ORIGIN_hex1303
5.062059 6.094828 4.851339 3.370373 5.255177
ORIGIN_hex1305 ORIGIN_hex1306 ORIGIN_hex1307 ORIGIN_hex1312 ORIGIN_hex1313
6.724970 6.749458 6.769132 5.213089 5.996087
ORIGIN_hex1314 ORIGIN_hex1315 ORIGIN_hex1316 ORIGIN_hex1317 ORIGIN_hex1318
4.673893 5.104713 3.343826 5.798451 5.897398
ORIGIN_hex1319 ORIGIN_hex1320 ORIGIN_hex1326 ORIGIN_hex1327 ORIGIN_hex1328
6.086378 6.852998 4.714199 5.558754 4.225752
ORIGIN_hex1329 ORIGIN_hex1330 ORIGIN_hex1331 ORIGIN_hex1332 ORIGIN_hex1333
6.072341 6.553098 6.141622 5.394134 6.290751
ORIGIN_hex1336 ORIGIN_hex1337 ORIGIN_hex1338 ORIGIN_hex1339 ORIGIN_hex1340
4.322423 5.095634 5.550748 3.746325 2.198248
ORIGIN_hex1341 ORIGIN_hex1342 ORIGIN_hex1343 ORIGIN_hex1344 ORIGIN_hex1345
5.464324 6.757933 6.050359 6.546974 7.625523
ORIGIN_hex1348 ORIGIN_hex1349 ORIGIN_hex1350 ORIGIN_hex1351 ORIGIN_hex1352
4.834591 5.320905 3.584154 3.109326 1.088784
ORIGIN_hex1353 ORIGIN_hex1354 ORIGIN_hex1355 ORIGIN_hex1356 ORIGIN_hex1357
6.298465 6.111035 6.642484 5.914339 6.447298
ORIGIN_hex1359 ORIGIN_hex1360 ORIGIN_hex1362 ORIGIN_hex1363 ORIGIN_hex1365
3.148806 5.374744 4.860817 2.563830 6.227816
ORIGIN_hex1366 ORIGIN_hex1367 ORIGIN_hex1368 ORIGIN_hex1369 ORIGIN_hex1370
5.924298 6.770207 7.084605 5.108004 5.338646
ORIGIN_hex1371 ORIGIN_hex1372 ORIGIN_hex1373 ORIGIN_hex1374 ORIGIN_hex1375
5.595088 6.083336 3.201310 3.238688 2.657040
ORIGIN_hex1376 ORIGIN_hex1377 ORIGIN_hex1378 ORIGIN_hex1379 ORIGIN_hex1382
6.387990 6.568276 6.859141 5.166307 4.812123
ORIGIN_hex1383 ORIGIN_hex1384 ORIGIN_hex1388 ORIGIN_hex1389 ORIGIN_hex1390
5.941699 4.944346 5.982516 7.656599 7.029447
ORIGIN_hex1391 ORIGIN_hex1392 ORIGIN_hex1393 ORIGIN_hex1394 ORIGIN_hex1395
6.388524 5.759311 5.057960 4.070232 2.580886
ORIGIN_hex1397 ORIGIN_hex1399 ORIGIN_hex1400 ORIGIN_hex1401 ORIGIN_hex1402
3.595449 6.162915 6.034858 3.629365 4.633325
ORIGIN_hex1404 ORIGIN_hex1405 ORIGIN_hex1406 ORIGIN_hex1409 ORIGIN_hex1410
5.009325 5.598983 6.232842 4.362552 -0.162738
ORIGIN_hex1411 ORIGIN_hex1412 ORIGIN_hex1413 ORIGIN_hex1414 ORIGIN_hex1415
5.850066 6.047567 2.173233 5.496955 3.069481
ORIGIN_hex1416 ORIGIN_hex1417 ORIGIN_hex1420 ORIGIN_hex1422 ORIGIN_hex1426
4.733961 4.849896 -0.561518 6.129023 4.975477
ORIGIN_hex1427 ORIGIN_hex1428 ORIGIN_hex1429 ORIGIN_hex1432 ORIGIN_hex1433
4.202285 5.085925 3.510367 1.313440 4.880805
ORIGIN_hex1434 ORIGIN_hex1437 ORIGIN_hex1438 ORIGIN_hex1439 ORIGIN_hex1442
6.751362 4.319667 5.954476 5.841735 5.011017
ORIGIN_hex1444 ORIGIN_hex1446 ORIGIN_hex1447 ORIGIN_hex1448 ORIGIN_hex1450
6.668492 5.180672 6.050154 5.619075 0.308803
ORIGIN_hex1451 ORIGIN_hex1456 ORIGIN_hex1457 ORIGIN_hex1458 ORIGIN_hex1459
2.436820 4.211080 6.217279 5.001105 6.092825
ORIGIN_hex1460 ORIGIN_hex1461 ORIGIN_hex1465 ORIGIN_hex1466 ORIGIN_hex1467
4.439191 4.878575 5.083938 5.946808 6.035122
ORIGIN_hex1468 ORIGIN_hex1469 ORIGIN_hex1470 ORIGIN_hex1471 ORIGIN_hex1475
5.171141 6.325169 4.985384 5.862115 5.132027
ORIGIN_hex1476 ORIGIN_hex1477 ORIGIN_hex1478 ORIGIN_hex1479 ORIGIN_hex1480
5.709415 4.585918 5.637774 5.992637 5.796694
ORIGIN_hex1481 ORIGIN_hex1484 ORIGIN_hex1485 ORIGIN_hex1486 ORIGIN_hex1487
3.574712 5.635757 5.734097 5.529503 5.856408
ORIGIN_hex1488 ORIGIN_hex1489 ORIGIN_hex1491 ORIGIN_hex1492 ORIGIN_hex1493
5.581573 5.815972 5.178396 6.013572 2.293219
ORIGIN_hex1494 ORIGIN_hex1495 ORIGIN_hex1496 ORIGIN_hex1497 ORIGIN_hex1499
6.744280 5.691858 6.349061 3.298486 5.814802
ORIGIN_hex1500 ORIGIN_hex1501 ORIGIN_hex1502 ORIGIN_hex1503 ORIGIN_hex1504
3.758283 4.496083 5.984023 4.158731 4.810434
ORIGIN_hex1506 ORIGIN_hex1507 ORIGIN_hex1508 ORIGIN_hex1509 ORIGIN_hex1510
4.807011 6.409430 5.288863 5.371370 5.208048
ORIGIN_hex1511 ORIGIN_hex1513 ORIGIN_hex1514 ORIGIN_hex1515 ORIGIN_hex1516
6.639534 3.075866 4.924024 3.863231 5.449857
ORIGIN_hex1517 ORIGIN_hex1518 ORIGIN_hex1522 ORIGIN_hex1523 ORIGIN_hex1524
6.075965 5.984041 4.046809 5.759634 5.748298
ORIGIN_hex1525 ORIGIN_hex1528 ORIGIN_hex1529 ORIGIN_hex1530 ORIGIN_hex1531
5.990897 4.676222 5.162629 6.091706 6.096389
ORIGIN_hex1532 ORIGIN_hex1534 ORIGIN_hex1535 ORIGIN_hex1536 ORIGIN_hex1537
5.874469 1.759580 4.564342 4.813797 5.775810
ORIGIN_hex1538 ORIGIN_hex1540 ORIGIN_hex1541 ORIGIN_hex1542 ORIGIN_hex1543
5.906891 2.152557 4.810922 6.035864 5.090731
ORIGIN_hex1544 ORIGIN_hex1546 ORIGIN_hex1547 ORIGIN_hex1548 ORIGIN_hex1549
5.333651 2.153984 0.899748 2.888695 4.062877
ORIGIN_hex1550 ORIGIN_hex1551 ORIGIN_hex1553 ORIGIN_hex1554 ORIGIN_hex1555
4.865783 1.995477 3.096286 4.157224 3.473194
ORIGIN_hex1556 ORIGIN_hex1557 ORIGIN_hex1563 ORIGIN_hex1564 ORIGIN_hex1565
3.807251 2.259716 3.786958 3.494627 2.996990
ORIGIN_hex1570 ORIGIN_hex1571 ORIGIN_hex1572 ORIGIN_hex1575 ORIGIN_hex1579
4.808206 1.945338 2.915020 5.805359 4.020119
ORIGIN_hex1583 ORIGIN_hex1584 ORIGIN_hex1587 ORIGIN_hex1588 ORIGIN_hex1592
3.628316 5.501597 4.904405 4.978869 5.042713
ORIGIN_hex1594 ORIGIN_hex1602 ORIGIN_hex1603 ORIGIN_hex1608 ORIGIN_hex1609
3.996199 -0.212174 3.805208 5.019173 4.958845
ORIGIN_hex1616 ORIGIN_hex1623 ORIGIN_hex1630 ORIGIN_hex1643 ORIGIN_hex1644
2.877373 4.051563 -2.208282 4.540494 5.845861
ORIGIN_hex1665 DESTIN_hex31 DESTIN_hex39 DESTIN_hex40 DESTIN_hex41
3.025064 -0.187576 2.278522 2.544351 -0.237904
DESTIN_hex49 DESTIN_hex50 DESTIN_hex51 DESTIN_hex52 DESTIN_hex59
-0.831975 1.968793 1.060073 0.972849 1.139654
DESTIN_hex60 DESTIN_hex61 DESTIN_hex62 DESTIN_hex63 DESTIN_hex72
-1.812486 0.606916 1.259920 -1.035603 -0.386674
DESTIN_hex73 DESTIN_hex74 DESTIN_hex75 DESTIN_hex83 DESTIN_hex84
1.712728 0.495647 -1.061720 0.710929 -0.142231
DESTIN_hex85 DESTIN_hex86 DESTIN_hex87 DESTIN_hex88 DESTIN_hex89
0.050692 -0.016798 -0.207337 -0.068475 -0.494837
DESTIN_hex96 DESTIN_hex97 DESTIN_hex99 DESTIN_hex100 DESTIN_hex101
-1.703752 0.059205 0.878363 -0.530372 -0.085813
DESTIN_hex112 DESTIN_hex113 DESTIN_hex114 DESTIN_hex124 DESTIN_hex125
-0.859497 -1.480781 -2.600253 -2.820572 -0.508959
DESTIN_hex126 DESTIN_hex135 DESTIN_hex136 DESTIN_hex137 DESTIN_hex145
-2.426458 1.658903 -0.275628 -0.651344 -0.525296
DESTIN_hex146 DESTIN_hex147 DESTIN_hex155 DESTIN_hex156 DESTIN_hex157
-1.532602 0.321893 -1.955133 -0.848893 -1.466001
DESTIN_hex168 DESTIN_hex169 DESTIN_hex170 DESTIN_hex181 DESTIN_hex182
1.011349 -0.489911 -0.975182 0.972728 -0.658577
DESTIN_hex183 DESTIN_hex197 DESTIN_hex198 DESTIN_hex199 DESTIN_hex213
-2.519065 0.957786 -0.381377 0.231234 0.057529
DESTIN_hex214 DESTIN_hex215 DESTIN_hex231 DESTIN_hex232 DESTIN_hex233
0.506952 0.483172 -2.815611 -1.907584 0.195582
DESTIN_hex249 DESTIN_hex250 DESTIN_hex252 DESTIN_hex265 DESTIN_hex266
0.039566 -0.678331 0.671413 0.652161 0.073165
DESTIN_hex267 DESTIN_hex268 DESTIN_hex269 DESTIN_hex283 DESTIN_hex284
0.393636 0.132072 1.439334 -1.630653 -0.175125
DESTIN_hex286 DESTIN_hex287 DESTIN_hex288 DESTIN_hex300 DESTIN_hex301
-5.007696 -0.732452 -6.341390 -0.023013 0.597229
DESTIN_hex302 DESTIN_hex303 DESTIN_hex304 DESTIN_hex319 DESTIN_hex320
-0.515704 -0.456819 -0.702850 -0.678971 -1.149451
DESTIN_hex321 DESTIN_hex322 DESTIN_hex323 DESTIN_hex334 DESTIN_hex335
-2.100774 1.825228 -6.362177 -1.759705 1.273782
DESTIN_hex336 DESTIN_hex337 DESTIN_hex339 DESTIN_hex340 DESTIN_hex351
-0.838483 -0.511374 -1.495990 -0.939236 1.491645
DESTIN_hex352 DESTIN_hex353 DESTIN_hex354 DESTIN_hex355 DESTIN_hex356
-0.391576 -0.533775 -0.242561 -2.040818 -3.428794
DESTIN_hex357 DESTIN_hex367 DESTIN_hex368 DESTIN_hex369 DESTIN_hex370
-3.597187 -0.473484 -0.740286 -1.904012 0.129137
DESTIN_hex371 DESTIN_hex373 DESTIN_hex374 DESTIN_hex375 DESTIN_hex377
-0.579523 -3.343109 -1.738363 -1.658665 -2.845712
DESTIN_hex385 DESTIN_hex386 DESTIN_hex387 DESTIN_hex388 DESTIN_hex390
1.001161 0.096877 0.043416 -1.265986 -2.708018
DESTIN_hex393 DESTIN_hex394 DESTIN_hex395 DESTIN_hex402 DESTIN_hex403
-2.686528 -0.807004 -1.634769 0.333962 -0.762848
DESTIN_hex404 DESTIN_hex405 DESTIN_hex407 DESTIN_hex411 DESTIN_hex412
1.343963 -0.987975 -3.418935 -3.763640 -3.025822
DESTIN_hex413 DESTIN_hex419 DESTIN_hex420 DESTIN_hex421 DESTIN_hex422
-1.694120 -1.128288 -0.346026 -0.424975 -0.898678
DESTIN_hex424 DESTIN_hex430 DESTIN_hex437 DESTIN_hex438 DESTIN_hex439
-5.709741 -3.647132 -1.566824 -1.126878 -1.635478
DESTIN_hex440 DESTIN_hex442 DESTIN_hex453 DESTIN_hex454 DESTIN_hex455
-1.781536 -1.043359 0.030305 -3.000408 -1.330545
DESTIN_hex456 DESTIN_hex471 DESTIN_hex472 DESTIN_hex473 DESTIN_hex474
1.034798 -0.213517 0.102928 -1.080671 0.079060
DESTIN_hex476 DESTIN_hex487 DESTIN_hex488 DESTIN_hex489 DESTIN_hex490
-0.930355 0.679860 -1.829050 -0.030506 -2.560693
DESTIN_hex504 DESTIN_hex505 DESTIN_hex506 DESTIN_hex508 DESTIN_hex518
-1.430268 -2.844977 -0.357997 -1.942458 -0.776971
DESTIN_hex521 DESTIN_hex522 DESTIN_hex524 DESTIN_hex533 DESTIN_hex534
-0.561137 -3.010794 -4.083158 0.756328 0.171510
DESTIN_hex536 DESTIN_hex537 DESTIN_hex539 DESTIN_hex549 DESTIN_hex550
-0.537185 -1.059692 -3.023655 -0.674295 -0.257481
DESTIN_hex551 DESTIN_hex552 DESTIN_hex554 DESTIN_hex555 DESTIN_hex559
-0.321796 -0.801919 -1.387247 -3.689474 -1.372026
DESTIN_hex562 DESTIN_hex564 DESTIN_hex565 DESTIN_hex566 DESTIN_hex567
-0.295076 -1.595243 -1.406230 -0.934724 -2.354647
DESTIN_hex568 DESTIN_hex569 DESTIN_hex577 DESTIN_hex579 DESTIN_hex580
-1.701569 -2.933371 -0.505739 -0.658553 0.949814
DESTIN_hex581 DESTIN_hex582 DESTIN_hex583 DESTIN_hex584 DESTIN_hex585
-0.888170 -1.588609 -4.040085 -1.435376 -1.136580
DESTIN_hex586 DESTIN_hex588 DESTIN_hex589 DESTIN_hex593 DESTIN_hex594
-2.049028 -0.398305 0.177980 -1.433955 -0.914339
DESTIN_hex595 DESTIN_hex596 DESTIN_hex597 DESTIN_hex598 DESTIN_hex599
0.297195 -1.180197 -0.492082 -1.294776 -1.480038
DESTIN_hex600 DESTIN_hex601 DESTIN_hex603 DESTIN_hex604 DESTIN_hex609
0.615211 -0.022594 -1.641160 -1.001708 -0.139007
DESTIN_hex610 DESTIN_hex611 DESTIN_hex612 DESTIN_hex613 DESTIN_hex614
0.456000 -1.342586 -0.167488 -1.327837 0.081230
DESTIN_hex615 DESTIN_hex616 DESTIN_hex617 DESTIN_hex618 DESTIN_hex619
-1.484294 -0.778361 -2.515123 -1.500650 -0.064653
DESTIN_hex620 DESTIN_hex625 DESTIN_hex626 DESTIN_hex627 DESTIN_hex628
-0.947770 -0.626885 -0.785043 0.593832 0.696592
DESTIN_hex629 DESTIN_hex630 DESTIN_hex631 DESTIN_hex632 DESTIN_hex633
0.172336 -2.930094 -1.042349 -3.160708 -2.513428
DESTIN_hex634 DESTIN_hex635 DESTIN_hex636 DESTIN_hex643 DESTIN_hex644
0.423642 -3.733362 -1.270835 0.213558 -1.735984
DESTIN_hex645 DESTIN_hex646 DESTIN_hex649 DESTIN_hex650 DESTIN_hex651
0.160192 -0.358780 -1.226304 -2.651879 0.640828
DESTIN_hex652 DESTIN_hex653 DESTIN_hex654 DESTIN_hex659 DESTIN_hex660
-3.256495 -1.617044 -1.778259 -0.301402 -0.741540
DESTIN_hex661 DESTIN_hex662 DESTIN_hex663 DESTIN_hex665 DESTIN_hex666
-0.252528 1.039575 -1.263705 -2.995773 -1.372388
DESTIN_hex668 DESTIN_hex669 DESTIN_hex670 DESTIN_hex676 DESTIN_hex677
-2.468633 -1.483162 -4.785086 -0.444806 -1.568342
DESTIN_hex678 DESTIN_hex680 DESTIN_hex681 DESTIN_hex682 DESTIN_hex683
-0.852887 -2.141149 -0.650363 -0.840485 0.886908
DESTIN_hex687 DESTIN_hex688 DESTIN_hex693 DESTIN_hex694 DESTIN_hex695
1.755743 -1.882406 -0.537605 0.172666 1.731014
DESTIN_hex696 DESTIN_hex697 DESTIN_hex698 DESTIN_hex699 DESTIN_hex700
-0.794165 -0.988788 -2.321381 0.317259 -2.510337
DESTIN_hex701 DESTIN_hex703 DESTIN_hex706 DESTIN_hex711 DESTIN_hex712
-1.252065 -0.440214 1.595070 0.649327 -0.419697
DESTIN_hex713 DESTIN_hex715 DESTIN_hex716 DESTIN_hex718 DESTIN_hex722
-1.101686 -0.554939 -2.578140 -1.663164 -1.947222
DESTIN_hex723 DESTIN_hex729 DESTIN_hex730 DESTIN_hex731 DESTIN_hex732
-1.940415 -0.028209 -0.118156 -1.914752 1.749286
DESTIN_hex733 DESTIN_hex735 DESTIN_hex736 DESTIN_hex737 DESTIN_hex739
0.958338 -1.376483 -0.056777 -1.999456 -0.850940
DESTIN_hex741 DESTIN_hex742 DESTIN_hex746 DESTIN_hex747 DESTIN_hex748
0.300068 -1.486463 0.892643 0.530864 0.219221
DESTIN_hex749 DESTIN_hex750 DESTIN_hex751 DESTIN_hex753 DESTIN_hex754
-1.407708 1.075039 -0.913603 -2.123474 -4.621326
DESTIN_hex758 DESTIN_hex759 DESTIN_hex760 DESTIN_hex764 DESTIN_hex766
-1.568644 -1.367470 -5.081470 1.108043 0.065792
DESTIN_hex767 DESTIN_hex769 DESTIN_hex775 DESTIN_hex777 DESTIN_hex778
-1.471439 -0.454027 0.217420 -1.462736 -0.728886
DESTIN_hex782 DESTIN_hex783 DESTIN_hex784 DESTIN_hex785 DESTIN_hex786
0.297740 0.560241 -0.697202 -2.268227 -1.120786
DESTIN_hex794 DESTIN_hex795 DESTIN_hex796 DESTIN_hex799 DESTIN_hex800
-4.140801 1.826242 -0.758004 -1.100986 0.688775
DESTIN_hex801 DESTIN_hex802 DESTIN_hex810 DESTIN_hex812 DESTIN_hex813
-1.427141 -1.263053 -3.601536 -0.647000 -1.209652
DESTIN_hex816 DESTIN_hex817 DESTIN_hex818 DESTIN_hex819 DESTIN_hex820
-0.108042 0.232969 0.467277 0.948886 -2.393455
DESTIN_hex821 DESTIN_hex827 DESTIN_hex829 DESTIN_hex830 DESTIN_hex831
-0.840801 0.885495 -0.208606 -1.478141 0.483431
DESTIN_hex835 DESTIN_hex836 DESTIN_hex837 DESTIN_hex838 DESTIN_hex847
0.175686 -1.457707 -1.288210 -1.763097 -1.372625
DESTIN_hex848 DESTIN_hex849 DESTIN_hex851 DESTIN_hex853 DESTIN_hex854
-1.258366 0.118397 1.399892 -0.362203 -0.973155
DESTIN_hex856 DESTIN_hex863 DESTIN_hex864 DESTIN_hex865 DESTIN_hex866
-0.280662 -1.368552 -2.614512 0.790513 0.167787
DESTIN_hex867 DESTIN_hex868 DESTIN_hex869 DESTIN_hex870 DESTIN_hex871
-0.336224 -0.554061 -0.348172 -0.604915 0.993697
DESTIN_hex873 DESTIN_hex882 DESTIN_hex883 DESTIN_hex884 DESTIN_hex885
-0.632120 -0.235719 -1.159151 0.275172 -1.141521
DESTIN_hex887 DESTIN_hex888 DESTIN_hex889 DESTIN_hex890 DESTIN_hex899
1.474487 0.599324 -0.833864 -1.323280 -2.312346
DESTIN_hex901 DESTIN_hex902 DESTIN_hex903 DESTIN_hex905 DESTIN_hex906
-0.709827 -0.295724 0.071707 -0.072823 -0.347068
DESTIN_hex907 DESTIN_hex909 DESTIN_hex910 DESTIN_hex917 DESTIN_hex920
0.141356 -0.131289 -1.066922 -4.400286 -0.804284
DESTIN_hex922 DESTIN_hex925 DESTIN_hex926 DESTIN_hex927 DESTIN_hex928
0.391778 -0.718079 0.809534 -0.993910 -1.335858
DESTIN_hex929 DESTIN_hex936 DESTIN_hex937 DESTIN_hex940 DESTIN_hex941
-0.759869 -2.373193 -1.556308 0.610909 0.461015
DESTIN_hex944 DESTIN_hex945 DESTIN_hex946 DESTIN_hex947 DESTIN_hex949
-0.624114 0.976707 0.253136 -1.554973 -0.792826
DESTIN_hex955 DESTIN_hex959 DESTIN_hex960 DESTIN_hex962 DESTIN_hex963
-4.903935 -0.570538 -1.334225 -0.654570 -0.355887
DESTIN_hex964 DESTIN_hex965 DESTIN_hex966 DESTIN_hex968 DESTIN_hex969
-0.120152 0.848161 -0.681642 0.066104 -1.941383
DESTIN_hex974 DESTIN_hex975 DESTIN_hex978 DESTIN_hex979 DESTIN_hex980
-5.873880 -0.858957 -1.628532 0.691112 -1.087186
DESTIN_hex982 DESTIN_hex983 DESTIN_hex984 DESTIN_hex985 DESTIN_hex986
-1.473992 1.132879 1.239657 -1.004800 0.116353
DESTIN_hex989 DESTIN_hex993 DESTIN_hex994 DESTIN_hex995 DESTIN_hex996
-3.396900 -1.110005 -0.189623 -2.883963 -1.822898
DESTIN_hex998 DESTIN_hex999 DESTIN_hex1002 DESTIN_hex1004 DESTIN_hex1005
-1.372265 -1.827336 0.279787 -0.772409 0.981871
DESTIN_hex1006 DESTIN_hex1008 DESTIN_hex1013 DESTIN_hex1015 DESTIN_hex1016
-1.718996 1.109555 0.854025 -1.389096 -2.545126
DESTIN_hex1017 DESTIN_hex1018 DESTIN_hex1019 DESTIN_hex1023 DESTIN_hex1024
-2.130731 -1.523610 -2.163008 -0.748781 -0.671741
DESTIN_hex1025 DESTIN_hex1026 DESTIN_hex1027 DESTIN_hex1028 DESTIN_hex1029
-0.416575 -0.256674 -0.610806 -1.780683 -4.337019
DESTIN_hex1031 DESTIN_hex1032 DESTIN_hex1034 DESTIN_hex1035 DESTIN_hex1036
-1.205166 -0.770476 -3.891320 -3.860456 -3.410768
DESTIN_hex1037 DESTIN_hex1038 DESTIN_hex1039 DESTIN_hex1044 DESTIN_hex1045
0.147540 0.097448 -2.530230 -0.937574 -0.532820
DESTIN_hex1046 DESTIN_hex1047 DESTIN_hex1048 DESTIN_hex1051 DESTIN_hex1052
-0.603058 -1.805604 -1.577971 -0.095131 -2.087544
DESTIN_hex1053 DESTIN_hex1056 DESTIN_hex1057 DESTIN_hex1058 DESTIN_hex1059
-1.795931 1.236606 -2.003475 -1.769629 -0.956578
DESTIN_hex1063 DESTIN_hex1065 DESTIN_hex1067 DESTIN_hex1068 DESTIN_hex1069
-4.213931 -2.148724 0.004580 -0.358382 -0.480451
DESTIN_hex1070 DESTIN_hex1071 DESTIN_hex1072 DESTIN_hex1073 DESTIN_hex1075
-0.191333 0.063898 -0.170140 -1.741346 -4.276327
DESTIN_hex1076 DESTIN_hex1077 DESTIN_hex1078 DESTIN_hex1079 DESTIN_hex1083
-0.923426 -1.069158 -2.101923 -3.185406 -0.008527
DESTIN_hex1085 DESTIN_hex1086 DESTIN_hex1088 DESTIN_hex1089 DESTIN_hex1090
0.052267 0.444581 -0.187942 -1.635748 -1.031417
DESTIN_hex1091 DESTIN_hex1092 DESTIN_hex1093 DESTIN_hex1095 DESTIN_hex1096
0.023734 -0.770180 -1.777684 -0.799744 1.152111
DESTIN_hex1097 DESTIN_hex1099 DESTIN_hex1103 DESTIN_hex1104 DESTIN_hex1106
-0.859875 -1.451295 0.889314 -0.316063 -0.093124
DESTIN_hex1107 DESTIN_hex1108 DESTIN_hex1109 DESTIN_hex1110 DESTIN_hex1111
0.429063 -0.916129 -0.698803 -0.474979 -2.196245
DESTIN_hex1112 DESTIN_hex1115 DESTIN_hex1116 DESTIN_hex1124 DESTIN_hex1125
-0.906949 -1.464549 -0.354671 0.088051 0.307905
DESTIN_hex1126 DESTIN_hex1127 DESTIN_hex1128 DESTIN_hex1129 DESTIN_hex1130
1.605676 -1.409942 -0.496332 -0.179479 0.380567
DESTIN_hex1131 DESTIN_hex1133 DESTIN_hex1134 DESTIN_hex1142 DESTIN_hex1143
0.261169 -1.669553 -1.358062 0.753845 -0.055452
DESTIN_hex1144 DESTIN_hex1145 DESTIN_hex1146 DESTIN_hex1147 DESTIN_hex1148
-0.450346 0.021174 1.395264 -1.389281 0.356906
DESTIN_hex1149 DESTIN_hex1152 DESTIN_hex1153 DESTIN_hex1161 DESTIN_hex1162
0.414702 -2.108574 -2.779994 -0.688409 0.056049
DESTIN_hex1163 DESTIN_hex1164 DESTIN_hex1165 DESTIN_hex1166 DESTIN_hex1168
-0.136670 -0.627496 -1.262064 1.111341 0.986058
DESTIN_hex1171 DESTIN_hex1178 DESTIN_hex1179 DESTIN_hex1180 DESTIN_hex1181
-1.498131 -1.426528 -1.016944 -0.747723 -0.936741
DESTIN_hex1182 DESTIN_hex1183 DESTIN_hex1187 DESTIN_hex1194 DESTIN_hex1196
-0.005293 0.481341 -2.250765 0.965399 -1.301274
DESTIN_hex1197 DESTIN_hex1198 DESTIN_hex1199 DESTIN_hex1200 DESTIN_hex1202
0.355002 -0.259856 -2.080257 -0.504153 -1.699738
DESTIN_hex1203 DESTIN_hex1205 DESTIN_hex1212 DESTIN_hex1213 DESTIN_hex1214
-1.555304 -4.145981 0.067330 -0.535484 -1.963146
DESTIN_hex1215 DESTIN_hex1216 DESTIN_hex1217 DESTIN_hex1218 DESTIN_hex1220
-1.288826 -1.602329 -0.624388 -4.886168 -3.638423
DESTIN_hex1221 DESTIN_hex1226 DESTIN_hex1227 DESTIN_hex1228 DESTIN_hex1229
-1.691882 -0.055065 -1.333599 0.496416 0.353840
DESTIN_hex1230 DESTIN_hex1231 DESTIN_hex1232 DESTIN_hex1233 DESTIN_hex1234
-1.971482 -1.624366 0.224762 0.308868 -2.270214
DESTIN_hex1235 DESTIN_hex1236 DESTIN_hex1243 DESTIN_hex1244 DESTIN_hex1245
-2.094781 -3.531048 0.654340 1.159343 -0.039985
DESTIN_hex1246 DESTIN_hex1247 DESTIN_hex1248 DESTIN_hex1249 DESTIN_hex1251
0.114568 -0.686034 -0.498346 -1.207343 -2.468917
DESTIN_hex1252 DESTIN_hex1257 DESTIN_hex1258 DESTIN_hex1259 DESTIN_hex1260
-2.942012 -0.408880 0.374564 0.024602 -1.646119
DESTIN_hex1261 DESTIN_hex1262 DESTIN_hex1263 DESTIN_hex1264 DESTIN_hex1265
-1.841832 -0.875779 0.324804 0.035140 -1.172555
DESTIN_hex1266 DESTIN_hex1267 DESTIN_hex1272 DESTIN_hex1273 DESTIN_hex1274
-0.377488 -2.643385 -0.687452 0.131725 0.833503
DESTIN_hex1275 DESTIN_hex1276 DESTIN_hex1277 DESTIN_hex1278 DESTIN_hex1279
-2.034147 1.385630 -1.487058 0.294141 -2.805710
DESTIN_hex1280 DESTIN_hex1281 DESTIN_hex1285 DESTIN_hex1286 DESTIN_hex1287
-1.829471 -3.185007 -2.427344 0.126983 -0.403375
DESTIN_hex1288 DESTIN_hex1289 DESTIN_hex1290 DESTIN_hex1291 DESTIN_hex1292
0.376118 -0.835152 -1.311672 -0.868330 -1.352454
DESTIN_hex1293 DESTIN_hex1299 DESTIN_hex1300 DESTIN_hex1301 DESTIN_hex1302
-1.502707 -0.888111 0.431569 0.511868 0.050869
DESTIN_hex1303 DESTIN_hex1305 DESTIN_hex1306 DESTIN_hex1307 DESTIN_hex1312
-1.259388 -0.323203 -0.886757 -2.916696 -0.097902
DESTIN_hex1313 DESTIN_hex1314 DESTIN_hex1315 DESTIN_hex1316 DESTIN_hex1317
0.457769 -0.510225 0.177524 -2.274774 1.017828
DESTIN_hex1318 DESTIN_hex1319 DESTIN_hex1320 DESTIN_hex1326 DESTIN_hex1327
-1.531133 -0.612148 -1.618577 -1.072228 0.531660
DESTIN_hex1328 DESTIN_hex1329 DESTIN_hex1330 DESTIN_hex1331 DESTIN_hex1332
0.354887 0.137880 -1.432078 -0.440864 -2.298769
DESTIN_hex1333 DESTIN_hex1336 DESTIN_hex1337 DESTIN_hex1338 DESTIN_hex1339
-2.313755 -0.593614 -0.611424 0.470173 1.209330
DESTIN_hex1340 DESTIN_hex1341 DESTIN_hex1342 DESTIN_hex1343 DESTIN_hex1344
-1.194138 -0.455336 0.847071 0.289346 -0.026378
DESTIN_hex1345 DESTIN_hex1348 DESTIN_hex1349 DESTIN_hex1350 DESTIN_hex1351
-1.873380 -0.311508 0.969602 1.053143 -0.117189
DESTIN_hex1352 DESTIN_hex1353 DESTIN_hex1354 DESTIN_hex1355 DESTIN_hex1356
0.464980 -0.445511 -1.260269 -1.548138 -1.376470
DESTIN_hex1357 DESTIN_hex1359 DESTIN_hex1360 DESTIN_hex1362 DESTIN_hex1363
-2.700981 -1.702041 -0.762592 1.075248 1.190088
DESTIN_hex1365 DESTIN_hex1366 DESTIN_hex1367 DESTIN_hex1368 DESTIN_hex1369
-1.870546 -1.757798 0.161190 -0.963849 -2.805688
DESTIN_hex1370 DESTIN_hex1371 DESTIN_hex1372 DESTIN_hex1373 DESTIN_hex1374
0.520915 0.797673 0.686915 -0.108649 -0.961940
DESTIN_hex1375 DESTIN_hex1376 DESTIN_hex1377 DESTIN_hex1378 DESTIN_hex1379
-2.904064 -2.120654 -1.436504 -1.136107 -3.279069
DESTIN_hex1382 DESTIN_hex1383 DESTIN_hex1384 DESTIN_hex1388 DESTIN_hex1389
-0.406285 0.564112 0.551784 -2.267988 0.236197
DESTIN_hex1390 DESTIN_hex1391 DESTIN_hex1392 DESTIN_hex1393 DESTIN_hex1394
0.315804 -1.922500 1.003571 -0.432362 -3.103383
DESTIN_hex1395 DESTIN_hex1397 DESTIN_hex1399 DESTIN_hex1400 DESTIN_hex1401
-1.709672 -0.003143 -1.959478 -2.042575 -2.545437
DESTIN_hex1402 DESTIN_hex1404 DESTIN_hex1405 DESTIN_hex1406 DESTIN_hex1409
-1.658344 -1.213940 0.385384 0.861235 0.628025
DESTIN_hex1410 DESTIN_hex1411 DESTIN_hex1412 DESTIN_hex1413 DESTIN_hex1414
-3.124612 -0.747080 -1.772746 -5.735420 -0.260439
DESTIN_hex1415 DESTIN_hex1416 DESTIN_hex1417 DESTIN_hex1420 DESTIN_hex1422
-2.217155 -0.370310 -0.325202 -3.600508 -2.203593
DESTIN_hex1426 DESTIN_hex1427 DESTIN_hex1428 DESTIN_hex1429 DESTIN_hex1432
-0.538531 0.192950 0.113722 -1.402282 -0.660051
DESTIN_hex1433 DESTIN_hex1434 DESTIN_hex1437 DESTIN_hex1438 DESTIN_hex1439
-2.578219 -2.032080 -0.227039 -0.192414 -0.175418
DESTIN_hex1442 DESTIN_hex1444 DESTIN_hex1446 DESTIN_hex1447 DESTIN_hex1448
0.218280 -2.113933 -0.444001 0.858567 -0.618548
DESTIN_hex1450 DESTIN_hex1451 DESTIN_hex1456 DESTIN_hex1457 DESTIN_hex1458
-3.167342 -2.084260 -1.004591 1.083493 -1.926783
DESTIN_hex1459 DESTIN_hex1460 DESTIN_hex1461 DESTIN_hex1465 DESTIN_hex1466
-0.096277 -1.189633 0.765159 -0.843354 0.679310
DESTIN_hex1467 DESTIN_hex1468 DESTIN_hex1469 DESTIN_hex1470 DESTIN_hex1471
0.346611 0.862811 -0.492275 -0.297030 0.758185
DESTIN_hex1475 DESTIN_hex1476 DESTIN_hex1477 DESTIN_hex1478 DESTIN_hex1479
-0.680713 -0.317021 -1.136572 -0.422127 -0.768994
DESTIN_hex1480 DESTIN_hex1481 DESTIN_hex1484 DESTIN_hex1485 DESTIN_hex1486
-0.810611 -2.587971 -0.934893 -0.617190 0.708782
DESTIN_hex1487 DESTIN_hex1488 DESTIN_hex1489 DESTIN_hex1491 DESTIN_hex1492
-0.945054 -1.931375 -0.546072 -1.396215 -0.393619
DESTIN_hex1493 DESTIN_hex1494 DESTIN_hex1495 DESTIN_hex1496 DESTIN_hex1497
-1.127898 1.858745 -1.147087 -0.745489 -1.659461
DESTIN_hex1499 DESTIN_hex1500 DESTIN_hex1501 DESTIN_hex1502 DESTIN_hex1503
-1.121160 -1.508867 -0.902250 0.640477 -2.739814
DESTIN_hex1504 DESTIN_hex1506 DESTIN_hex1507 DESTIN_hex1508 DESTIN_hex1509
-0.381068 -1.048943 1.228320 0.876308 -1.292845
DESTIN_hex1510 DESTIN_hex1511 DESTIN_hex1513 DESTIN_hex1514 DESTIN_hex1515
-1.298504 1.667095 -0.823532 -1.033630 1.040498
DESTIN_hex1516 DESTIN_hex1517 DESTIN_hex1518 DESTIN_hex1522 DESTIN_hex1523
0.032889 0.791694 -1.338887 -1.826134 -0.491926
DESTIN_hex1524 DESTIN_hex1525 DESTIN_hex1528 DESTIN_hex1529 DESTIN_hex1530
-1.145420 -0.654614 0.180800 -0.962139 -0.101159
DESTIN_hex1531 DESTIN_hex1532 DESTIN_hex1534 DESTIN_hex1535 DESTIN_hex1536
-0.328821 -1.498652 -1.381550 0.627064 -0.502396
DESTIN_hex1537 DESTIN_hex1538 DESTIN_hex1540 DESTIN_hex1541 DESTIN_hex1542
-0.831358 -0.825101 1.111700 -0.708465 -0.341168
DESTIN_hex1543 DESTIN_hex1544 DESTIN_hex1546 DESTIN_hex1547 DESTIN_hex1548
-0.606940 -2.000755 1.147585 -1.858561 0.706459
DESTIN_hex1549 DESTIN_hex1550 DESTIN_hex1551 DESTIN_hex1553 DESTIN_hex1554
-1.935275 0.256976 -0.912716 1.359094 0.975123
DESTIN_hex1555 DESTIN_hex1556 DESTIN_hex1557 DESTIN_hex1563 DESTIN_hex1564
-0.974662 -1.431716 0.907818 -1.635899 -0.909504
DESTIN_hex1565 DESTIN_hex1570 DESTIN_hex1571 DESTIN_hex1572 DESTIN_hex1575
-0.350175 -0.187507 -1.566796 -1.021091 0.949570
DESTIN_hex1579 DESTIN_hex1583 DESTIN_hex1584 DESTIN_hex1587 DESTIN_hex1588
-0.755174 -1.509938 1.255164 -0.149198 0.490300
DESTIN_hex1592 DESTIN_hex1594 DESTIN_hex1602 DESTIN_hex1603 DESTIN_hex1608
1.482876 -0.729626 -2.850976 -1.101575 1.970379
DESTIN_hex1609 DESTIN_hex1616 DESTIN_hex1623 DESTIN_hex1630 DESTIN_hex1643
1.545360 0.222512 1.862799 -1.140616 -2.955193
DESTIN_hex1644 DESTIN_hex1665 dist
1.474527 0.574490 -1.719430
Degrees of Freedom: 51925 Total (i.e. Null); 50333 Residual
Null Deviance: 73540000
Residual Deviance: 19840000 AIC: 20110000Now that we have fit three different spatial interaction models, we will now save the fitted values resulted from each model into a new dataset called fitted_flow_weekday_morn. These fitted values represent the estimated flows from each model.
orcSIM_fitted <- as.data.frame(orcSIM_weekday_morn$fitted.values)
colnames(orcSIM_fitted) <- "ORCEstimatedFlow"
fitted_flow_weekday_morn <- cbind(flow_data_weekday_morn,orcSIM_fitted)
desSIM_fitted <- as.data.frame(desSIM_weekday_morn$fitted.values)
colnames(desSIM_fitted) <- "DESEstimatedFlow"
fitted_flow_weekday_morn <- cbind(fitted_flow_weekday_morn,desSIM_fitted)
dbcSIM_fitted <- as.data.frame(dbcSIM_weekday_morn$fitted.values)
colnames(dbcSIM_fitted) <- "DBCEstimatedFlow"
fitted_flow_weekday_morn <- cbind(fitted_flow_weekday_morn,dbcSIM_fitted)4.10 Original Constraint Flow Estimation Map
Looking at the model outputs above, the results are not intuitive enough for users, especially those without background to understand and interpret. In this session, we will test and try different visualization approaches to better present the model results.
particularly, we are interested to test a R package called stplanr which provides functions for transport modelling such as creating geographic “desire lines” from origin-destination data.
pacman::p_load(stplanr)Desire lines are a powerful tool for visualizing the flow of movement between different locations. However, they are not suitable for visualizing intra-regional movements, where both the origin and destination belong to a single spatial unit. Therefore, we need to filter out intra-regional trajectories from our dataset first.
od_plot <- fitted_flow_weekday_morn[fitted_flow_weekday_morn$ORIGIN_hex!=fitted_flow_weekday_morn$DESTIN_hex,]Next, we will create a flowLine object which compiles all the desire lines from our dataset. This is done using the od2line() function from the stplanr package.
flowLine <- od2line(flow = od_plot,
zones = hex_grid_pa_sz,
zone_code = "index")
flowLine <- st_join(flowLine, hex_grid_pa_sz,by = "index")Next, we will filter out the desire lines with flow volume less than 5000. This is to ensure that we only visualize the most significant flow lines.
Reflection
Prototyping Thoughts
During the initial stages of my prototyping, I hadn’t considered the idea of filtering the desire lines based on flow volume. However, as I iterated and refined my approach, I realized that having too many lines on a single map could potentially limit its interpretability, making it difficult to discern meaningful patterns. This led me to the conclusion that it might be more effective to focus on flows with significant volume. By doing so, I could reduce the clutter and make the map more readable, allowing for a more detailed and focused analysis.
orc_flowLine <- flowLine %>% filter(ORCEstimatedFlow > 5000)Next, we will generate maps for inflow and outflow, akin to our previous approach. However, this time, we will utilize the fitted values derived from the Origin Constrained SIM model. The process involves aggregating the dataset based on either the ORIGIN_hex or DESTIN_hex. Subsequently, we will integrate this aggregated data with the hexagonal grid data for visualization purposes.
orc_fitted_inflow <- aggregate(fitted_flow_weekday_morn$ORCEstimatedFlow, by=list(Category=fitted_flow_weekday_morn$DESTIN_hex), FUN=sum)
colnames(orc_fitted_inflow) <- c("index", "Estimated_InFlow")
orc_fitted_inflow_hex <- left_join(hex_grid_pa_sz, orc_fitted_inflow, by = 'index')
orc_fitted_inflow_hex$Estimated_InFlow <- ifelse(is.na(orc_fitted_inflow_hex$Estimated_InFlow), 0, orc_fitted_inflow_hex$Estimated_InFlow)
orc_fitted_outflow <- aggregate(fitted_flow_weekday_morn$ORCEstimatedFlow, by=list(Category=fitted_flow_weekday_morn$ORIGIN_hex), FUN=sum)
colnames(orc_fitted_outflow) <- c("index", "Estimated_OutFlow")
orc_fitted_outflow_hex <- left_join(hex_grid_pa_sz, orc_fitted_outflow, by = 'index')
orc_fitted_outflow_hex$Estimated_OutFlow <- ifelse(is.na(orc_fitted_outflow_hex$Estimated_OutFlow), 0, orc_fitted_outflow_hex$Estimated_OutFlow)Finally, we will use the appropriate tmap functions to create an interactive map with four layers. Each layer serves a unique purpose and adds a different dimension to our visualization.
hex_grid_pa_sz: This layer serves as the base map for the analytical hexagons used in our modeling. It forms the foundation upon which we’ll overlay our desire lines and other data.orc_fitted_inflow_hex: This layer represents the estimated volume of inflow for each hexagonal unit, as determined by our Origin Constrained Spatial Interaction Model (SIM). It will give us a visual representation of where people are coming from.orc_fitted_outflow_hex: Similarly, this layer represents the estimated volume of outflow for each hexagonal unit, also based on our Origin Constrained SIM. This will help us understand where people are going.orc_flowLine: This layer represents the estimated desire lines resulting from our Origin Constrained SIM. These lines will be represented in differing colors and line widths based on trip volume, providing a visual representation of the flow between different hexagons.
tmap_mode("view")
tm_shape(hex_grid_pa_sz) +
tm_fill(col="#f2ffff",
id = "PLN_AREA_N") +
tm_borders(col = "grey") +
tm_shape(orc_fitted_inflow_hex) +
tm_fill(col = "Estimated_InFlow",
palette = c("#f2ffff","#f9f777","#f8d673","#f89974","#D66779","#b977cb","#7977f3","#57bfc0"),
style = "fixed",
breaks = c(0,1,100,1000,10000,100000,500000,1000000,5000000),
title = "Estimated Inflow Volume",
id = "Estimated_InFlow")+
tm_borders(col = "grey") +
tm_shape(orc_fitted_outflow_hex) +
tm_fill(col = "Estimated_OutFlow",
palette = c("#f2ffff","#f9f777","#f8d673","#f89974","#D66779","#b977cb","#7977f3","#57bfc0"),
style = "fixed",
breaks = c(0,1,100,1000,10000,100000,500000,1000000,5000000),
title = "Estimated Outflow Volume",
id = "Estimated_OutFlow")+
tm_borders(col = "grey") +
tm_shape(orc_flowLine) +
tm_lines(lwd = "ORCEstimatedFlow",
col = "ORCEstimatedFlow",
palette = c("#f8d673","#f89974","#D66779","#b977cb","#7977f3","#57bfc0"),
style = "pretty",
scale = c(1,2,3,4,5,7,9),
n = 6,
title.lwd = "Orgin Constrained Flow",
id = "ORCEstimatedFlow")
Reflection
Prototyping Thoughts
During my prototyping process, I’ve been considering the user experience quite a bit. Even though I’ve overlaid all four layers in the current stage, I’m contemplating a more interactive approach for our Shiny application by allowing them to choose the layers they want to see. They could select one layer at a time or any combination of layers, depending on what they’re interested in. This way, they can customize the map to their preferences and focus on the data that’s most relevant to them.
This approach would not only make the application more interactive but also more user-friendly. Users could explore different layers at their own pace, delve deeper into the ones they find interesting, and ultimately gain a more personalized understanding of the data.
4.11 Destination Constraint Flow Estimation Map
Similar to what we did with origin constrained SIM model, we will follow the same procedure for plotting destination constrained SIM model results.
des_flowLine <- flowLine %>% filter(DESEstimatedFlow > 5000)des_fitted_inflow <- aggregate(fitted_flow_weekday_morn$DESEstimatedFlow, by=list(Category=fitted_flow_weekday_morn$DESTIN_hex), FUN=sum)
colnames(des_fitted_inflow) <- c("index", "Estimated_InFlow")
des_fitted_inflow_hex <- left_join(hex_grid_pa_sz, des_fitted_inflow, by = 'index')
des_fitted_inflow_hex$Estimated_InFlow <- ifelse(is.na(des_fitted_inflow_hex$Estimated_InFlow), 0, des_fitted_inflow_hex$Estimated_InFlow)
des_fitted_outflow <- aggregate(fitted_flow_weekday_morn$DESEstimatedFlow, by=list(Category=fitted_flow_weekday_morn$ORIGIN_hex), FUN=sum)
colnames(des_fitted_outflow) <- c("index", "Estimated_OutFlow")
des_fitted_outflow_hex <- left_join(hex_grid_pa_sz, des_fitted_outflow, by = 'index')
des_fitted_outflow_hex$Estimated_OutFlow <- ifelse(is.na(des_fitted_outflow_hex$Estimated_OutFlow), 0, des_fitted_outflow_hex$Estimated_OutFlow)tmap_mode("view")
tm_shape(hex_grid_pa_sz) +
tm_fill(col="#f2ffff",
id = "PLN_AREA_N") +
tm_borders(col = "grey") +
tm_shape(des_fitted_inflow_hex) +
tm_fill(col = "Estimated_InFlow",
palette = c("#f2ffff","#f9f777","#f8d673","#f89974","#D66779","#b977cb","#7977f3","#57bfc0"),
style = "fixed",
breaks = c(0,1,100,1000,10000,100000,500000,1000000,5000000),
title = "Estimated Inflow Volume",
id = "Estimated_InFlow")+
tm_borders(col = "grey") +
tm_shape(des_fitted_outflow_hex) +
tm_fill(col = "Estimated_OutFlow",
palette = c("#f2ffff","#f9f777","#f8d673","#f89974","#D66779","#b977cb","#7977f3","#57bfc0"),
style = "fixed",
breaks = c(0,1,100,1000,10000,100000,500000,1000000,5000000),
title = "Estimated Outflow Volume",
id = "Estimated_OutFlow")+
tm_borders(col = "grey") +
tm_shape(orc_flowLine) +
tm_lines(lwd = "DESEstimatedFlow",
col = "DESEstimatedFlow",
palette = c("#f8d673","#f89974","#D66779","#b977cb","#7977f3","#57bfc0"),
style = "pretty",
scale = c(1,2,3,4,5,7,9),
n = 6,
title.lwd = "Destination Constrained Flow",
id = "DESEstimatedFlow")4.12 Doubly Constraint Flow Estimation Map
Similar to what we did with origin constrained SIM model, we will follow the same procedure for plotting doubly constrained SIM model results.
dbc_flowLine <- flowLine %>% filter(DBCEstimatedFlow > 5000)dbc_fitted_inflow <- aggregate(fitted_flow_weekday_morn$DBCEstimatedFlow, by=list(Category=fitted_flow_weekday_morn$DESTIN_hex), FUN=sum)
colnames(dbc_fitted_inflow) <- c("index", "Estimated_InFlow")
dbc_fitted_inflow_hex <- left_join(hex_grid_pa_sz, orc_fitted_inflow, by = 'index')
dbc_fitted_inflow_hex$Estimated_InFlow <- ifelse(is.na(dbc_fitted_inflow_hex$Estimated_InFlow), 0, dbc_fitted_inflow_hex$Estimated_InFlow)
dbc_fitted_outflow <- aggregate(fitted_flow_weekday_morn$DBCEstimatedFlow, by=list(Category=fitted_flow_weekday_morn$ORIGIN_hex), FUN=sum)
colnames(dbc_fitted_outflow) <- c("index", "Estimated_OutFlow")
dbc_fitted_outflow_hex <- left_join(hex_grid_pa_sz, orc_fitted_outflow, by = 'index')
dbc_fitted_outflow_hex$Estimated_OutFlow <- ifelse(is.na(dbc_fitted_outflow_hex$Estimated_OutFlow), 0, dbc_fitted_outflow_hex$Estimated_OutFlow)tmap_mode("view")
tm_shape(hex_grid_pa_sz) +
tm_fill(col="#f2ffff",
id = "PLN_AREA_N") +
tm_borders(col = "grey") +
tm_shape(dbc_fitted_inflow_hex) +
tm_fill(col = "Estimated_InFlow",
palette = c("#f2ffff","#f9f777","#f8d673","#f89974","#D66779","#b977cb","#7977f3","#57bfc0"),
style = "fixed",
breaks = c(0,1,100,1000,10000,100000,500000,1000000,5000000),
title = "Estimated Inflow Volume",
id = "Estimated_InFlow")+
tm_borders(col = "grey") +
tm_shape(dbc_fitted_outflow_hex) +
tm_fill(col = "Estimated_OutFlow",
palette = c("#f2ffff","#f9f777","#f8d673","#f89974","#D66779","#b977cb","#7977f3","#57bfc0"),
style = "fixed",
breaks = c(0,1,100,1000,10000,100000,500000,1000000,5000000),
title = "Estimated Outflow Volume",
id = "Estimated_OutFlow")+
tm_borders(col = "grey") +
tm_shape(orc_flowLine) +
tm_lines(lwd = "DBCEstimatedFlow",
col = "DBCEstimatedFlow",
palette = c("#f8d673","#f89974","#D66779","#b977cb","#7977f3","#57bfc0"),
style = "pretty",
scale = c(1,2,3,4,5,7,9),
n = 6,
title.lwd = "Destination Constrained Flow",
id = "DBCEstimatedFlow")
Reflection
Prototyping Thoughts
During my prototyping process, I spent some time to think about the organization of the models. Initially, I considered having a separate tabset for each model type. However, upon reflection, I believe it might be more beneficial to have the model type as one of the calibration inputs and combine everything on one page. The advantage of this approach is that it allows users to stack layers not just from one model, but across different models as well. For instance, they could stack desire flows from all three models and analyze the differences in the results. This would be challenging if we have each tabset for each model than the user will have to keep swtiching from one tab to another just to compare the results.
4.13 Zooming to Specific Planning Area & Subzones
Similar to what we did in earlier sections, we can also create planning area and subzone specific maps. In the following example, I tried to prototype using destination constrained SIM model.
Reflection
Prototyping Thoughts
For the purpose of prototyping, I’ve been using the destination constrained Spatial Interaction Model (SIM). However, in the actual Shiny application, I plan to give users the flexibility to choose both the model type and the planning/area or subzone they want to use for their analysis.
Additionally, I’m considering allowing users to specify the time period they’re interested in - whether it’s the morning or evening peak, or weekday or weekend/holiday. However, in this exercise we are only using weekday morning dataset, it is not possible to do it here. But the actual application will be designed to handle different time periods.
des_flowLine_map_pa <- function(pa_input){
des_flowLine_temp <- flowLine %>% filter(PLN_AREA_N == pa_input, DBCEstimatedFlow > 1000)
des_fitted_inflow_hex <- des_fitted_inflow_hex %>% filter(PLN_AREA_N == pa_input)
des_fitted_outflow_hex <- des_fitted_outflow_hex %>% filter(PLN_AREA_N == pa_input)
tmap_mode("view")
tm_shape(hex_grid_pa_sz) +
tm_fill(col="#f2ffff") +
tm_borders(col = "grey") +
tm_shape(des_fitted_inflow_hex) +
tm_fill(col = "Estimated_InFlow",
palette = c("#f2ffff","#f9f777","#f8d673","#f89974","#D66779","#b977cb","#7977f3","#57bfc0"),
style = "fixed",
breaks = c(0,1,100,1000,10000,100000,500000,1000000,5000000),
title = "Estimated Inflow Volume",
id = "Estimated_InFlow")+
tm_borders(col = "grey") +
tm_shape(des_fitted_outflow_hex) +
tm_fill(col = "Estimated_OutFlow",
palette = c("#f2ffff","#f9f777","#f8d673","#f89974","#D66779","#b977cb","#7977f3","#57bfc0"),
style = "fixed",
breaks = c(0,1,100,1000,10000,100000,500000,1000000,5000000),
title = "Estimated Outflow Volume",
id = "Estimated_OutFlow")+
tm_borders(col = "grey") +
tm_shape(des_flowLine_temp) +
tm_lines(lwd = "DESEstimatedFlow",
col = "DESEstimatedFlow",
palette = c("#f8d673","#f89974","#D66779","#b977cb","#7977f3","#57bfc0"),
style = "pretty",
scale = c(1,2,3,4,5,7,9),
n = 6,
title.lwd = "Destination Constrained Flow",
id = "DESEstimatedFlow")
}des_flowLine_map_sz <- function(sz_input){
des_flowLine_temp <- flowLine %>% filter(SUBZONE_N == sz_input, DBCEstimatedFlow > 1000)
des_fitted_inflow_hex <- des_fitted_inflow_hex %>% filter(SUBZONE_N == sz_input)
des_fitted_outflow_hex <- des_fitted_outflow_hex %>% filter(SUBZONE_N == sz_input)
tmap_mode("view")
tm_shape(hex_grid_pa_sz) +
tm_fill(col="#f2ffff") +
tm_borders(col = "grey") +
tm_shape(des_fitted_inflow_hex) +
tm_fill(col = "Estimated_InFlow",
palette = c("#f2ffff","#f9f777","#f8d673","#f89974","#D66779","#b977cb","#7977f3","#57bfc0"),
style = "fixed",
breaks = c(0,1,100,1000,10000,100000,500000,1000000,5000000),
title = "Estimated Inflow Volume",
id = "Estimated_InFlow")+
tm_borders(col = "grey") +
tm_shape(des_fitted_outflow_hex) +
tm_fill(col = "Estimated_OutFlow",
palette = c("#f2ffff","#f9f777","#f8d673","#f89974","#D66779","#b977cb","#7977f3","#57bfc0"),
style = "fixed",
breaks = c(0,1,100,1000,10000,100000,500000,1000000,5000000),
title = "Estimated Outflow Volume",
id = "Estimated_OutFlow")+
tm_borders(col = "grey") +
tm_shape(des_flowLine_temp) +
tm_lines(lwd = "DESEstimatedFlow",
col = "DESEstimatedFlow",
palette = c("#f8d673","#f89974","#D66779","#b977cb","#7977f3","#57bfc0"),
style = "pretty",
scale = c(1,2,3,4,5,7,9),
n = 6,
title.lwd = "Destination Constrained Flow",
id = "DESEstimatedFlow")
}
Reflection
Prototyping Thoughts
During my prototyping process, I’ve made an adjustment to the filtering based on flow volume. Initially, I was filtering out data with a flow volume less than 5000. However, I realized that some subzones and planning areas might have a lower flow volume, which could lead to errors if the maximum flow is less than this threshold filter.
To avoid such errors, I decided to reduce the threshold to 1000. This allows for a more inclusive analysis, capturing data from areas with lower flow volumes. However, I’m aware that there could still be instances where the flow is even less than 1000, which could still potentially lead to errors.
While I haven’t addressed this issue in the current stage, I’m actively thinking about ways to handle this in the final Shiny app.
As a demonstration, we call the des_flowLine_map_pa() function with “WOODLANDS” and the des_flowLine_map_sz() function with “NATURE RESERVE” as inputs. to test whether the functions works well and produce desired outcomes.
des_flowLine_map_pa("WOODLANDS")des_flowLine_map_sz("NATURE RESERVE")4.14 Push-Pull Factors
Beyond looking at the estimated flow volumes, spatial interaction modelling also offers valuable insights by providing coefficient estimates for explanatory variables, both at the origin and destination locations.
In particular, the origin-constrained SIM is instrumental in identifying the ‘pull’ factors of the destination. These factors represent conditions or circumstances that draw people from multiple origins towards the destination.
Conversely, the destination-constrained SIM sheds light on the ‘push’ factors at the origin. These factors represent conditions or circumstances that encourage people to leave the origin and move to multiple destinations.
Looking at the coefficient estimates of these push-pull factors, we can find correlation between the flow volume and the increase or decrease in the value of these factors.
To do visualisations and analysis with push-pull factors, we will first extract fitted coefficient values from origin-constrained and destination-constrained SIM models first.
pull_factors <- tibble::rownames_to_column(as.data.frame(orcSIM_weekday_morn$coefficients), "factors")
colnames(pull_factors) <- c("factors", "coefficients")
pull_factors <- pull_factors[grep("^(d_)", pull_factors$factors), ]push_factors <- tibble::rownames_to_column(as.data.frame(desSIM_weekday_morn$coefficients), "factors")
colnames(push_factors) <- c("factors", "coefficients")
push_factors <- push_factors[grep("^(o_)", push_factors$factors), ]Let’s look at the data a bit.
pull_factors$factors [1] "d_biz_count" "d_school_count" "d_fin_count"
[4] "d_hc_count" "d_busstop_count" "d_housing_count"
[7] "d_leisure_recre_count" "d_retail_count" "d_entertn_count"
[10] "d_food_bev_count"
Reflection
Prototyping Thoughts
During my prototyping process, I’ve come to realize the importance of clarity and interpretability. It’s not just about presenting the data, but also about making it understandable and meaningful to the user.
While I understand what each of these factor values means, it may not be as clear for everyone else. Especially without the context of the data, terms like d_hc_count can be confusing - and we cannot assume that they will know hc refers to healthcare!
With this in mind, I’ve decided to update these values to be more explicit and straightforward. Instead of using abbreviations, I’ll use clear, descriptive names that accurately represent what each value stands for. This way, users can easily understand what they’re looking at, making the application more user-friendly and informative.
We will now update the factors values in pull_factors dataset from abbreviations to long form as below.
pull_factors$factors <- c("Business", "School", "Financial Institute","Healthcare","Bus Stop", "Housing", "Leisure/Recreation", "Retail", "Entertainment", "Food & Beverages")push_factors$factors [1] "o_biz_count" "o_school_count" "o_fin_count"
[4] "o_hc_count" "o_busstop_count" "o_housing_count"
[7] "o_leisure_recre_count" "o_retail_count" "o_entertn_count"
[10] "o_food_bev_count" We will do the same for factors values in push_factors dataset.
push_factors$factors <- c("Business", "School", "Financial Institute","Healthcare","Bus Stop", "Housing", "Leisure/Recreation", "Retail", "Entertainment", "Food & Beverages")Now that we have prepared all the data, we will plot bar graphs using relevant ggplot2 functions.
ggplot(data = pull_factors,
aes(x = coefficients,
y = reorder(factors, coefficients),
fill = factors)) +
geom_bar(stat="identity", show.legend = FALSE) +
xlab("Coefficient Estimate") +
ylab("Pull Factors of Destination")
ggplot(data = push_factors,
aes(x = coefficients,
y = reorder(factors, coefficients),
fill = factors)) +
geom_bar(stat="identity", show.legend = FALSE) +
xlab("Coefficient Estimate") +
ylab("Push Factors of Origin")
Reflection
Prototyping Thoughts
Visualizing the coefficient estimates using bar graphs, instead of simple tables, indeed enhances interpretability. It provides a clear picture of not only the magnitude (absolute value) but also the direction (positive or negative) of each coefficient estimate.
For example, in push factor graph above, we can clearly see that an increase in business establishments corresponds to a decrease in pushing people away, indicating that areas with more businesses tend to attract more people. On the other hand, an increase in financial institutes corresponds to an increase in pushing people away, suggesting that areas with more financial institutes might be less attractive for some reason.
This kind of visual representation makes it much easier to understand and interpret the results of the analysis.
4.15 Exploring User Input Options for Shiny Application
Reflection on what we explored in the exercise above, we will use two tabset - Flow Estimation Map and Push-Pull Factors to visualise the results.
4.15.1 Flow Estimation Map
For Flow Estimation Map tabset, we may include the following user specification and model calibration options for our Shiny application.
| Input | Options |
|---|---|
| Model Type | Origin-Constrained, Destination-Constrained, Doubly Constrained |
| Time Period | Weekday - Morning , Weekday - Evening, Weekend/Holiday - Morning, Weekend/Holiday - Evening |
| Result Layer | O-D Desire Line, Fitted Inflow Map, Fitted Outflow Map |
| Zooming Level | Overall (Singapore) , Planning Area, Subzone |
| Area of Interest |
|
Below is a rough outline of how the user interface for this tabset might look like.
4.15.1 Push-Pull Factors
For Push-Pull Factors tabset, we may include the following user specification and model calibration options for our Shiny application. Note that we remove the specification for Model Type as push-pull factors cannot be derived from a single SIM model.
| Input | Options |
|---|---|
| Time Period | Weekday - Morning , Weekday - Evening, Weekend/Holiday - Morning, Weekend/Holiday - Evening |
| Zooming Level | Overall (Singapore) , Planning Area, Subzone |
| Area of Interest |
|
Below is a rough outline of how the user interface for this tabset might look like.
4.16 Comparing Estimated Flows from Different Models
In this section, we are comparing the performance of the three Spatial Interaction Models (SIMs) we have fitted above: the origin constrained SIM, the destination constrained SIM, and the doubly constrained SIM. To achieve it, we will explore an R packaged called performance which provides functions for assessment of model quality and performance.
pacman::p_load(performance)Firstly, we will a list of the three models we have fitted: the origin constrained SIM (orcSIM_weekday_morn), the destination constrained SIM (desSIM_weekday_morn), and the doubly constrained SIM (dbcSIM_weekday_morn).
We will then use the compare_performance function to compare the models based on the RMSE. The RMSE is a measure of the differences between the values predicted by a model and the values actually observed.
model_list <- list(originConstrained=orcSIM_weekday_morn,
destinConstrained=desSIM_weekday_morn,
doublyConstrained=dbcSIM_weekday_morn)
compare_performance(model_list, metrics = "RMSE")# Comparison of Model Performance Indices
Name | Model | RMSE
------------------------------------
originConstrained | glm | 1498.442
destinConstrained | glm | 1468.283
doublyConstrained | glm | 1137.973Next, we will create scatter plots to compare the observed flows against the estimated flows from each model.
ggplot(data = fitted_flow_weekday_morn,
aes(x = ORCEstimatedFlow,
y = TOTAL_TRIPS)) +
geom_point() +
geom_smooth(method = lm) +
coord_cartesian(xlim=c(0,100000),
ylim=c(0,100000)) +
labs(title = "Observed vs. Fitted Values for Origin Constrained SIM",
x = "Fitted Values", y = "Observed Values")
ggplot(data = fitted_flow_weekday_morn,
aes(x = DESEstimatedFlow,
y = TOTAL_TRIPS)) +
geom_point() +
geom_smooth(method = lm) +
coord_cartesian(xlim=c(0,100000),
ylim=c(0,100000)) +
labs(title = "Observed vs. Fitted Values for Destination Constrained SIM",
x = "Fitted Values", y = "Observed Values")
ggplot(data = fitted_flow_weekday_morn,
aes(x = DBCEstimatedFlow,
y = TOTAL_TRIPS)) +
geom_point() +
geom_smooth(method = lm) +
coord_cartesian(xlim=c(0,100000),
ylim=c(0,100000)) +
labs(title = "Observed vs. Fitted Values for Doubly Constrained SIM",
x = "Fitted Values", y = "Observed Values")
Reflection
Prototyping Thoughts
As I’ve been working on the prototyping process, I’ve had some thoughts on whether or not to add the section on model comparison. While observed vs fitted value plots are essential in research for validating models, I realized they might not be as relevant or intuitive for everyone when used in a geospatial application. Given that the users of our Shiny application may not have a research background, such plots could potentially confuse them. Therefore, I’ve decided to focus on features that enhance the interpretability and usability of the application.
5.0 Proposed Shiny Application User Interface Storyboard
Below, I’m excited to present the finalized mock-up storyboard of the Shiny Application. I have focused on three specific tabsets that I have tested and explored throughout this exercise - Inflow/Outflow Map, Flow Estimation Map, and Push/Pull Factors. Not only will I present the user interface layout, but I will also show how different outputs would look like based on various user calibration inputs.
5.1 Inflow/Outflow Map
5.1.1 Inflow/Outflow Map for Singapore Overall
.png)
.png)
5.1.2 Inflow/Outflow Map for Planning Area/Subzone Zooming
.png)
5.2 Flow Estimation Map
5.2.1 Origin-Constrained Flow Estimation Maps
.png)
.png)
.png)
5.2.2 Destination-Constrained Flow Estimation Maps
5.2.3 Doubly-Constrained Flow Estimation Maps
5.2.4 Flow Estimation Maps for Planning Area/Subzone Zooming
.png)
5.3 Push-Pull Factors
6.0 Conclusion
Transitioning from research-oriented tasks to an analytical application, as required in this exercise, presented a unique set of challenges. Instead of focusing on the components of research studies, I shifted my attention to the elements of a typical data dashboard and the user's perception of the information presented therein. This exercise, while demanding, provided a valuable opportunity for learning through trial and error, significantly enhancing my data visualization skills.